C++ NonbondedForce::setEwaldErrorTolerance方法代码示例

void testPMEParameters() {
    // Create a cloud of random point charges.

    const int numParticles = 51;
    const double boxWidth = 4.7;
    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(NonbondedForce::PME);
    ReferencePlatform platform;
    
    // Compute the energy with an error tolerance of 1e-3.

    force->setEwaldErrorTolerance(1e-3);
    VerletIntegrator integrator1(0.01);
    Context context1(system, integrator1, platform);
    context1.setPositions(positions);
    double energy1 = context1.getState(State::Energy).getPotentialEnergy();
    
    // Try again with an error tolerance of 1e-4.

    force->setEwaldErrorTolerance(1e-4);
    VerletIntegrator integrator2(0.01);
    Context context2(system, integrator2, platform);
    context2.setPositions(positions);
    double energy2 = context2.getState(State::Energy).getPotentialEnergy();
    
    // Now explicitly set the parameters.  These should match the values that were
    // used for tolerance 1e-3.

    force->setPMEParameters(2.49291157051793, 32, 32, 32);
    VerletIntegrator integrator3(0.01);
    Context context3(system, integrator3, platform);
    context3.setPositions(positions);
    double energy3 = context3.getState(State::Energy).getPotentialEnergy();
    ASSERT_EQUAL_TOL(energy1, energy3, 1e-6);
    ASSERT(fabs((energy1-energy2)/energy1) > 1e-5);
}

void testEwald2Ions() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->addParticle(-1.0, 1, 0);
    nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
    const double cutoff = 2.0;
    nonbonded->setCutoffDistance(cutoff);
    nonbonded->setEwaldErrorTolerance(TOL);
    system.setDefaultPeriodicBoxVectors(Vec3(6, 0, 0), Vec3(0, 6, 0), Vec3(0, 0, 6));
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(3.048000,2.764000,3.156000);
    positions[1] = Vec3(2.809000,2.888000,2.571000);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();

    ASSERT_EQUAL_VEC(Vec3(-123.711,  64.1877, -302.716), forces[0], 10*TOL);
    ASSERT_EQUAL_VEC(Vec3( 123.711, -64.1877,  302.716), forces[1], 10*TOL);
    ASSERT_EQUAL_TOL(-217.276, state.getPotentialEnergy(), 0.01/*10*TOL*/);
}

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 testWaterSystem() {
    ReferencePlatform platform;
    System system;
    static int numParticles = 648;
    const double boxSize = 1.86206;

    for (int i = 0 ; i < numParticles ; i++)
    {
       system.addParticle(1.0);
    }
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    for (int i = 0 ; i < numParticles/3 ; i++)
    {
      nonbonded->addParticle(-0.82, 1, 0);
      nonbonded->addParticle(0.41, 1, 0);
      nonbonded->addParticle(0.41, 1, 0);
    }
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    const double cutoff = 0.8;
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    nonbonded->setEwaldErrorTolerance(EWALD_TOL);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    #include "water.dat"
    context.setPositions(positions);
    State state1 = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state1.getForces();

// Take a small step in the direction of the energy gradient.
    
    double norm = 0.0;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 f = state1.getForces()[i];
        norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
    }


    norm = std::sqrt(norm);
    const double delta = 1e-3;
    double step = delta/norm;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 p = positions[i];
        Vec3 f = state1.getForces()[i];
        positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
    }
    context.setPositions(positions);
    
    // See whether the potential energy changed by the expected amount.
    
    nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
    State state2 = context.getState(State::Energy);
    ASSERT_EQUAL_TOL(norm, (state2.getPotentialEnergy()-state1.getPotentialEnergy())/delta, 0.01)


}

void testSerialization() {
    // Create a Force.

    NonbondedForce force;
    force.setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    force.setCutoffDistance(2.0);
    force.setEwaldErrorTolerance(1e-3);
    force.setReactionFieldDielectric(50.0);
    force.setUseDispersionCorrection(false);
    force.addParticle(1, 0.1, 0.01);
    force.addParticle(0.5, 0.2, 0.02);
    force.addParticle(-0.5, 0.3, 0.03);
    force.addException(0, 1, 2, 0.5, 0.1);
    force.addException(1, 2, 0.2, 0.4, 0.2);

    // Serialize and then deserialize it.

    stringstream buffer;
    XmlSerializer::serialize<NonbondedForce>(&force, "Force", buffer);
    NonbondedForce* copy = XmlSerializer::deserialize<NonbondedForce>(buffer);

    // Compare the two forces to see if they are identical.

    NonbondedForce& force2 = *copy;
    ASSERT_EQUAL(force.getNonbondedMethod(), force2.getNonbondedMethod());
    ASSERT_EQUAL(force.getCutoffDistance(), force2.getCutoffDistance());
    ASSERT_EQUAL(force.getEwaldErrorTolerance(), force2.getEwaldErrorTolerance());
    ASSERT_EQUAL(force.getReactionFieldDielectric(), force2.getReactionFieldDielectric());
    ASSERT_EQUAL(force.getUseDispersionCorrection(), force2.getUseDispersionCorrection());
    ASSERT_EQUAL(force.getNumParticles(), force2.getNumParticles());
    for (int i = 0; i < force.getNumParticles(); i++) {
        double charge1, sigma1, epsilon1;
        double charge2, sigma2, epsilon2;
        force.getParticleParameters(i, charge1, sigma1, epsilon1);
        force2.getParticleParameters(i, charge2, sigma2, epsilon2);
        ASSERT_EQUAL(charge1, charge2);
        ASSERT_EQUAL(sigma1, sigma2);
        ASSERT_EQUAL(epsilon1, epsilon2);
    }
    ASSERT_EQUAL(force.getNumExceptions(), force2.getNumExceptions());
    for (int i = 0; i < force.getNumExceptions(); i++) {
        int a1, a2, b1, b2;
        double charge1, sigma1, epsilon1;
        double charge2, sigma2, epsilon2;
        force.getExceptionParameters(i, a1, b1, charge1, sigma1, epsilon1);
        force2.getExceptionParameters(i, a2, b2, charge2, sigma2, epsilon2);
        ASSERT_EQUAL(a1, a2);
        ASSERT_EQUAL(b1, b2);
        ASSERT_EQUAL(charge1, charge2);
        ASSERT_EQUAL(sigma1, sigma2);
        ASSERT_EQUAL(epsilon1, epsilon2);
    }
}

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 testEwaldExact() {

//    Use a NaCl crystal to compare the calculated and Madelung energies

    const int numParticles = 1000;
    const double cutoff = 1.0;
    const double boxSize = 2.82;

    ReferencePlatform platform;
    System system;

    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(22.99);
    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(35.45);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(1.0, 1.0,0.0);
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(-1.0, 1.0,0.0);
    nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    nonbonded->setEwaldErrorTolerance(EWALD_TOL);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    #include "nacl_crystal.dat"
    context.setPositions(positions);

    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();

//   The potential energy of an ion in a crystal is 
//   E = - (M*e^2/ 4*pi*epsilon0*a0),
//   where 
//   M            :    Madelung constant (dimensionless, for FCC cells such as NaCl it is 1.7476)
//   e            :    1.6022 × 10−19 C
//   4*pi*epsilon0:     1.112 × 10−10 C²/(J m)
//   a0           :    0.282 x 10-9 m (perfect cell)
// 
//   E is then the energy per pair of ions, so for our case
//   E has to be divided by 2 (per ion), multiplied by N(avogadro), multiplied by number of particles, and divided by 1000 for kJ
    double exactEnergy        = - (1.7476 * 1.6022e-19 * 1.6022e-19  * 6.02214e+23 * numParticles) / (1.112e-10 * 0.282e-9 * 2 * 1000);
    //cout << "exact\t\t: " << exactEnergy << endl;
    //cout << "calc\t\t: " << state.getPotentialEnergy() << endl;
    ASSERT_EQUAL_TOL(exactEnergy, state.getPotentialEnergy(), 100*EWALD_TOL);

}

void testEwaldPME(bool includeExceptions) {

//      Use amorphous NaCl system for the tests

    const int numParticles = 894;
    const double cutoff = 1.2;
    const double boxSize = 3.00646;
    double tol = 1e-5;

    ReferencePlatform reference;
    System system;
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
    nonbonded->setCutoffDistance(cutoff);
    nonbonded->setEwaldErrorTolerance(tol);

    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(22.99);
    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(35.45);
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(1.0, 1.0,0.0);
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(-1.0, 1.0,0.0);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    system.addForce(nonbonded);

    vector<Vec3> positions(numParticles);
#include "nacl_amorph.dat"
    if (includeExceptions) {
        // Add some exclusions.

        for (int i = 0; i < numParticles-1; i++) {
            Vec3 delta = positions[i]-positions[i+1];
            if (sqrt(delta.dot(delta)) < 0.5*cutoff)
                nonbonded->addException(i, i+1, i%2 == 0 ? 0.0 : 0.5, 1.0, 0.0);
        }
    }

//    (1)  Check whether the Reference and CPU platforms agree when using Ewald Method

    VerletIntegrator integrator1(0.01);
    VerletIntegrator integrator2(0.01);
    Context cpuContext(system, integrator1, platform);
    Context referenceContext(system, integrator2, reference);
    cpuContext.setPositions(positions);
    referenceContext.setPositions(positions);
    State cpuState = cpuContext.getState(State::Forces | State::Energy);
    State referenceState = referenceContext.getState(State::Forces | State::Energy);
    tol = 1e-2;
    for (int i = 0; i < numParticles; i++) {
        ASSERT_EQUAL_VEC(referenceState.getForces()[i], cpuState.getForces()[i], tol);
    }
    tol = 1e-5;
    ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), cpuState.getPotentialEnergy(), tol);

//    (2) Check whether Ewald method in CPU is self-consistent

    double norm = 0.0;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 f = cpuState.getForces()[i];
        norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
    }

    norm = std::sqrt(norm);
    const double delta = 5e-3;
    double step = delta/norm;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 p = positions[i];
        Vec3 f = cpuState.getForces()[i];
        positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
    }
    VerletIntegrator integrator3(0.01);
    Context cpuContext2(system, integrator3, platform);
    cpuContext2.setPositions(positions);

    tol = 1e-2;
    State cpuState2 = cpuContext2.getState(State::Energy);
    ASSERT_EQUAL_TOL(norm, (cpuState2.getPotentialEnergy()-cpuState.getPotentialEnergy())/delta, tol)

//    (3)  Check whether the Reference and CPU platforms agree when using PME

    nonbonded->setNonbondedMethod(NonbondedForce::PME);
    cpuContext.reinitialize();
    referenceContext.reinitialize();
    cpuContext.setPositions(positions);
    referenceContext.setPositions(positions);
    cpuState = cpuContext.getState(State::Forces | State::Energy);
    referenceState = referenceContext.getState(State::Forces | State::Energy);
    tol = 1e-2;
    for (int i = 0; i < numParticles; i++) {
        ASSERT_EQUAL_VEC(referenceState.getForces()[i], cpuState.getForces()[i], tol);
    }
    tol = 1e-5;
    ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), cpuState.getPotentialEnergy(), tol);

//    (4) Check whether PME method in CPU is self-consistent

    norm = 0.0;
    for (int i = 0; i < numParticles; ++i) {
//.........这里部分代码省略.........

void testSerialization() {
    // Create a Force.

    NonbondedForce force;
    force.setForceGroup(3);
    force.setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    force.setSwitchingDistance(1.5);
    force.setUseSwitchingFunction(true);
    force.setCutoffDistance(2.0);
    force.setEwaldErrorTolerance(1e-3);
    force.setReactionFieldDielectric(50.0);
    force.setUseDispersionCorrection(false);
    double alpha = 0.5;
    int nx = 3, ny = 5, nz = 7;
    force.setPMEParameters(alpha, nx, ny, nz);
    double dalpha = 0.8;
    int dnx = 4, dny = 6, dnz = 7;
    force.setLJPMEParameters(dalpha, dnx, dny, dnz);
    force.addParticle(1, 0.1, 0.01);
    force.addParticle(0.5, 0.2, 0.02);
    force.addParticle(-0.5, 0.3, 0.03);
    force.addException(0, 1, 2, 0.5, 0.1);
    force.addException(1, 2, 0.2, 0.4, 0.2);
    force.addGlobalParameter("scale1", 1.0);
    force.addGlobalParameter("scale2", 2.0);
    force.addParticleParameterOffset("scale1", 2, 1.5, 2.0, 2.5);
    force.addExceptionParameterOffset("scale2", 1, -0.1, -0.2, -0.3);

    // Serialize and then deserialize it.

    stringstream buffer;
    XmlSerializer::serialize<NonbondedForce>(&force, "Force", buffer);
    NonbondedForce* copy = XmlSerializer::deserialize<NonbondedForce>(buffer);

    // Compare the two forces to see if they are identical.

    NonbondedForce& force2 = *copy;
    ASSERT_EQUAL(force.getForceGroup(), force2.getForceGroup());
    ASSERT_EQUAL(force.getNonbondedMethod(), force2.getNonbondedMethod());
    ASSERT_EQUAL(force.getSwitchingDistance(), force2.getSwitchingDistance());
    ASSERT_EQUAL(force.getUseSwitchingFunction(), force2.getUseSwitchingFunction());
    ASSERT_EQUAL(force.getCutoffDistance(), force2.getCutoffDistance());
    ASSERT_EQUAL(force.getEwaldErrorTolerance(), force2.getEwaldErrorTolerance());
    ASSERT_EQUAL(force.getReactionFieldDielectric(), force2.getReactionFieldDielectric());
    ASSERT_EQUAL(force.getUseDispersionCorrection(), force2.getUseDispersionCorrection());
    ASSERT_EQUAL(force.getNumParticles(), force2.getNumParticles());
    ASSERT_EQUAL(force.getNumExceptions(), force2.getNumExceptions());
    ASSERT_EQUAL(force.getNumGlobalParameters(), force2.getNumGlobalParameters());
    ASSERT_EQUAL(force.getNumParticleParameterOffsets(), force2.getNumParticleParameterOffsets());
    ASSERT_EQUAL(force.getNumExceptionParameterOffsets(), force2.getNumExceptionParameterOffsets());
    double alpha2;
    int nx2, ny2, nz2;
    force2.getPMEParameters(alpha2, nx2, ny2, nz2);
    ASSERT_EQUAL(alpha, alpha2);
    ASSERT_EQUAL(nx, nx2);
    ASSERT_EQUAL(ny, ny2);
    ASSERT_EQUAL(nz, nz2);    
    double dalpha2;
    int dnx2, dny2, dnz2;
    force2.getLJPMEParameters(dalpha2, dnx2, dny2, dnz2);
    ASSERT_EQUAL(dalpha, dalpha2);
    ASSERT_EQUAL(dnx, dnx2);
    ASSERT_EQUAL(dny, dny2);
    ASSERT_EQUAL(dnz, dnz2);
    for (int i = 0; i < force.getNumGlobalParameters(); i++) {
        ASSERT_EQUAL(force.getGlobalParameterName(i), force2.getGlobalParameterName(i));
        ASSERT_EQUAL(force.getGlobalParameterDefaultValue(i), force2.getGlobalParameterDefaultValue(i));
    }
    for (int i = 0; i < force.getNumParticleParameterOffsets(); i++) {
        int index1, index2;
        string param1, param2;
        double charge1, sigma1, epsilon1;
        double charge2, sigma2, epsilon2;
        force.getParticleParameterOffset(i, param1, index1, charge1, sigma1, epsilon1);
        force2.getParticleParameterOffset(i, param2, index2, charge2, sigma2, epsilon2);
        ASSERT_EQUAL(index1, index1);
        ASSERT_EQUAL(param1, param2);
        ASSERT_EQUAL(charge1, charge2);
        ASSERT_EQUAL(sigma1, sigma2);
        ASSERT_EQUAL(epsilon1, epsilon2);
    }
    for (int i = 0; i < force.getNumExceptionParameterOffsets(); i++) {
        int index1, index2;
        string param1, param2;
        double charge1, sigma1, epsilon1;
        double charge2, sigma2, epsilon2;
        force.getExceptionParameterOffset(i, param1, index1, charge1, sigma1, epsilon1);
        force2.getExceptionParameterOffset(i, param2, index2, charge2, sigma2, epsilon2);
        ASSERT_EQUAL(index1, index1);
        ASSERT_EQUAL(param1, param2);
        ASSERT_EQUAL(charge1, charge2);
        ASSERT_EQUAL(sigma1, sigma2);
        ASSERT_EQUAL(epsilon1, epsilon2);
    }
    for (int i = 0; i < force.getNumParticles(); i++) {
        double charge1, sigma1, epsilon1;
        double charge2, sigma2, epsilon2;
        force.getParticleParameters(i, charge1, sigma1, epsilon1);
        force2.getParticleParameters(i, charge2, sigma2, epsilon2);
        ASSERT_EQUAL(charge1, charge2);
//.........这里部分代码省略.........

void ReferenceCalcMBPolElectrostaticsForceKernel::initialize(const OpenMM::System& system, const MBPolElectrostaticsForce& force) {

    numElectrostatics   = force.getNumElectrostatics();

    charges.resize(numElectrostatics);
    tholes.resize(5*numElectrostatics);
    dampingFactors.resize(numElectrostatics);
    polarity.resize(numElectrostatics);
    axisTypes.resize(numElectrostatics);
    multipoleAtomZs.resize(numElectrostatics);
    multipoleAtomXs.resize(numElectrostatics);
    multipoleAtomYs.resize(numElectrostatics);
    multipoleAtomCovalentInfo.resize(numElectrostatics);

    int dipoleIndex      = 0;
    int quadrupoleIndex  = 0;
    int tholeIndex       = 0;
    int maxCovalentRange = 0;
    double totalCharge   = 0.0;
    for( int ii = 0; ii < numElectrostatics; ii++ ){

        // multipoles

        int axisType, multipoleAtomZ, multipoleAtomX, multipoleAtomY;
        double charge, dampingFactorD, polarityD;
        std::vector<double> dipolesD;
        std::vector<double> tholesD;
        force.getElectrostaticsParameters(ii, charge, axisType, multipoleAtomZ, multipoleAtomX, multipoleAtomY,
                                     tholesD, dampingFactorD, polarityD );

        totalCharge                       += charge;
        axisTypes[ii]                      = axisType;
        multipoleAtomZs[ii]                = multipoleAtomZ;
        multipoleAtomXs[ii]                = multipoleAtomX;
        multipoleAtomYs[ii]                = multipoleAtomY;

        charges[ii]                        = static_cast<RealOpenMM>(charge);

        dampingFactors[ii]                 = static_cast<RealOpenMM>(dampingFactorD);
        polarity[ii]                       = static_cast<RealOpenMM>(polarityD);

        tholes[tholeIndex++]             = static_cast<RealOpenMM>(tholesD[0]);
        tholes[tholeIndex++]             = static_cast<RealOpenMM>(tholesD[1]);
        tholes[tholeIndex++]             = static_cast<RealOpenMM>(tholesD[2]);
        tholes[tholeIndex++]             = static_cast<RealOpenMM>(tholesD[3]);
        tholes[tholeIndex++]             = static_cast<RealOpenMM>(tholesD[4]);

        // covalent info

        std::vector< std::vector<int> > covalentLists;
        force.getCovalentMaps(ii, covalentLists );
        multipoleAtomCovalentInfo[ii] = covalentLists;

    }

    polarizationType = force.getPolarizationType();
    if( polarizationType == MBPolElectrostaticsForce::Mutual ){
        mutualInducedMaxIterations = force.getMutualInducedMaxIterations();
        mutualInducedTargetEpsilon = force.getMutualInducedTargetEpsilon();
    }

    includeChargeRedistribution = force.getIncludeChargeRedistribution();

    // PME

    nonbondedMethod  = force.getNonbondedMethod();
    if( nonbondedMethod == MBPolElectrostaticsForce::PME ){
        usePme     = true;
        alphaEwald = force.getAEwald();
        cutoffDistance = force.getCutoffDistance();
        force.getPmeGridDimensions(pmeGridDimension);
        if (pmeGridDimension[0] == 0 || alphaEwald == 0.0) {
            NonbondedForce nb;
            nb.setEwaldErrorTolerance(force.getEwaldErrorTolerance());
            nb.setCutoffDistance(force.getCutoffDistance());
            int gridSizeX, gridSizeY, gridSizeZ;
            NonbondedForceImpl::calcPMEParameters(system, nb, alphaEwald, gridSizeX, gridSizeY, gridSizeZ);
            pmeGridDimension[0] = gridSizeX;
            pmeGridDimension[1] = gridSizeY;
            pmeGridDimension[2] = gridSizeZ;
            std::cout << "Computed PME parameters for MBPolElectrostaticsForce, alphaEwald:" <<
                    alphaEwald << " pmeGrid: " <<  gridSizeX << "," <<  gridSizeY << ","<<  gridSizeZ << std::endl;
        }    
    } else {
        usePme = false;
    }
    return;
}

void testPME(bool triclinic) {
    // Create a cloud of random point charges.

    const int numParticles = 51;
    const double boxWidth = 5.0;
    const double cutoff = 1.0;
    Vec3 boxVectors[3];
    if (triclinic) {
        boxVectors[0] = Vec3(boxWidth, 0, 0);
        boxVectors[1] = Vec3(0.2*boxWidth, boxWidth, 0);
        boxVectors[2] = Vec3(-0.3*boxWidth, -0.1*boxWidth, boxWidth);
    }
    else {
        boxVectors[0] = Vec3(boxWidth, 0, 0);
        boxVectors[1] = Vec3(0, boxWidth, 0);
        boxVectors[2] = Vec3(0, 0, boxWidth);
    }
    System system;
    system.setDefaultPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
    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(NonbondedForce::PME);
    force->setCutoffDistance(cutoff);
    force->setReciprocalSpaceForceGroup(1);
    force->setEwaldErrorTolerance(1e-4);
    
    // Compute the reciprocal space forces with the reference platform.
    
    Platform& platform = Platform::getPlatformByName("Reference");
    VerletIntegrator integrator(0.01);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    State refState = context.getState(State::Forces | State::Energy, false, 1<<1);
    
    // Now compute them with the optimized kernel.
    
    double alpha;
    int gridx, gridy, gridz;
    NonbondedForceImpl::calcPMEParameters(system, *force, alpha, gridx, gridy, gridz, false);
    CpuCalcPmeReciprocalForceKernel pme(CalcPmeReciprocalForceKernel::Name(), platform);
    IO io;
    double sumSquaredCharges = 0;
    for (int i = 0; i < numParticles; i++) {
        io.posq.push_back(positions[i][0]);
        io.posq.push_back(positions[i][1]);
        io.posq.push_back(positions[i][2]);
        double charge, sigma, epsilon;
        force->getParticleParameters(i, charge, sigma, epsilon);
        io.posq.push_back(charge);
        sumSquaredCharges += charge*charge;
    }
    double ewaldSelfEnergy = -ONE_4PI_EPS0*alpha*sumSquaredCharges/sqrt(M_PI);
    pme.initialize(gridx, gridy, gridz, numParticles, alpha, true);
    pme.beginComputation(io, boxVectors, true);
    double energy = pme.finishComputation(io);

    // See if they match.
    
    ASSERT_EQUAL_TOL(refState.getPotentialEnergy(), energy+ewaldSelfEnergy, 1e-3);
    for (int i = 0; i < numParticles; i++)
        ASSERT_EQUAL_VEC(refState.getForces()[i], Vec3(io.force[4*i], io.force[4*i+1], io.force[4*i+2]), 1e-3);
}

void testEwaldPME() {

    double tol = 1e-5;
    const double boxSize = 3.00646;
    const double cutoff = 1.2;
    const int numParticles = 894;

//      Use amorphous NaCl system
//      The particles are simple charges, no VdW interactions

    ReferencePlatform platform;
    System system;
    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(22.99);
    for (int i = 0; i < numParticles/2; i++)
        system.addParticle(35.45);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(1.0, 1.0,0.0);
    for (int i = 0; i < numParticles/2; i++)
        nonbonded->addParticle(-1.0, 1.0,0.0);
    nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    nonbonded->setEwaldErrorTolerance(EWALD_TOL);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(numParticles);
    #include "nacl_amorph.dat"
    context.setPositions(positions);

    State state1 = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces1 = state1.getForces();

//   (1)   CHECK EXACT VALUE OF EWALD ENERGY (Against Gromacs output)

    tol = 1e-4;
    ASSERT_EQUAL_TOL(-3.82047e+05, state1.getPotentialEnergy(), tol);

//   (2)   CHECK WHETHER THE EWALD FORCES ARE THE SAME AS THE GROMACS OUTPUT
//         these are forces for alpha: 2.82756, kmax(x/y/z) = 11
  
    tol = 1e-2;
//    #include "nacl_amorph_GromacsForcesEwald.dat"

//   (3)   CHECK SELF-CONSISTENCY

    // Take a small step in the direction of the energy gradient.

    double norm = 0.0;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 f = state1.getForces()[i];
        norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
    }


    norm = std::sqrt(norm);
    const double delta = 1e-2;
    double step = delta/norm;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 p = positions[i];
        Vec3 f = state1.getForces()[i];
        positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
    }
    context.setPositions(positions);
    
    // See whether the potential energy changed by the expected amount.
    
    State state2 = context.getState(State::Energy);
    ASSERT_EQUAL_TOL(norm, (state2.getPotentialEnergy()-state1.getPotentialEnergy())/delta, fabs(EWALD_TOL*state2.getPotentialEnergy()/(state2.getPotentialEnergy()-state1.getPotentialEnergy())))

//   (4)   CHECK EXACT VALUE OF PME ENERGY 

    nonbonded->setNonbondedMethod(NonbondedForce::PME);
    nonbonded->setEwaldErrorTolerance(PME_TOL);
    context.reinitialize();
    #include "nacl_amorph.dat"
    context.setPositions(positions);
    State state3 = context.getState(State::Forces | State::Energy);

//  Gromacs PME energy for the same mesh
    tol = 1e-4;
    ASSERT_EQUAL_TOL(-3.82047e+05, state3.getPotentialEnergy(), tol);

//   (5) CHECK WHETHER PME FORCES ARE THE SAME AS THE GROMACS OUTPUT USING EWALD

    tol = 1e-1;
//    #include "nacl_amorph_GromacsForcesEwald.dat"

//   (6) CHECK PME FOR SELF-CONSISTENCY

    // Take a small step in the direction of the energy gradient.
    
    norm = 0.0;
    for (int i = 0; i < numParticles; ++i) {
        Vec3 f = state3.getForces()[i];
        norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
    }
    norm = std::sqrt(norm);
//.........这里部分代码省略.........