TestCudaCustomIntegrator.cpp

/* -------------------------------------------------------------------------- *
 *                                   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) 2008-2013 Stanford University and the Authors.      *
 * Authors: Peter Eastman                                                     *
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/**
 * This tests the CUDA implementation of CustomIntegrator.
 */

#include "openmm/internal/AssertionUtilities.h"
#include "openmm/Context.h"
#include "CudaPlatform.h"
#include "openmm/AndersenThermostat.h"
#include "openmm/HarmonicBondForce.h"
#include "openmm/NonbondedForce.h"
#include "openmm/System.h"
#include "openmm/CustomIntegrator.h"
#include "SimTKOpenMMRealType.h"
#include "sfmt/SFMT.h"
#include <iostream>
#include <vector>

using namespace OpenMM;
using namespace std;

CudaPlatform platform;

const double TOL = 1e-5;

/**
 * Test a simple leapfrog integrator on a single bond.
 */
void testSingleBond() {
    System system;
    system.addParticle(2.0);
    system.addParticle(2.0);
    const double dt = 0.01;
    CustomIntegrator integrator(dt);
    integrator.addComputePerDof("v", "v+dt*f/m");
    integrator.addComputePerDof("x", "x+dt*v");
    integrator.setKineticEnergyExpression("m*v1*v1/2; v1=v+0.5*dt*f/m");
    HarmonicBondForce* forceField = new HarmonicBondForce();
    forceField->addBond(0, 1, 1.5, 1);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(-1, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    context.setPositions(positions);
    vector<Vec3> velocities(2);
    velocities[0] = Vec3(-0.5*dt*0.5*0.5, 0, 0);
    velocities[1] = Vec3(0.5*dt*0.5*0.5, 0, 0);
    context.setVelocities(velocities);
    
    // This is simply a harmonic oscillator, so compare it to the analytical solution.
    
    const double freq = 1.0;;
    for (int i = 0; i < 1000; ++i) {
        State state = context.getState(State::Positions | State::Velocities | State::Energy);
        double time = state.getTime();
        double expectedDist = 1.5+0.5*std::cos(freq*time);
        ASSERT_EQUAL_VEC(Vec3(-0.5*expectedDist, 0, 0), state.getPositions()[0], 1e-4);
        ASSERT_EQUAL_VEC(Vec3(0.5*expectedDist, 0, 0), state.getPositions()[1], 1e-4);
        double expectedSpeed = -0.5*freq*std::sin(freq*(time-dt/2));
        ASSERT_EQUAL_VEC(Vec3(-0.5*expectedSpeed, 0, 0), state.getVelocities()[0], 1e-4);
        ASSERT_EQUAL_VEC(Vec3(0.5*expectedSpeed, 0, 0), state.getVelocities()[1], 1e-4);
        double energy = state.getKineticEnergy()+state.getPotentialEnergy();
        ASSERT_EQUAL_TOL(0.5*0.5*0.5, energy, 1e-4);
        integrator.step(1);
    }
}

/**
 * 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);
    }
}

/**
 * Test an integrator that applies constraints directly to velocities.
 */
void testVelocityConstraints() {
    const int numParticles = 10;
    System system;
    CustomIntegrator integrator(0.002);
    integrator.addPerDofVariable("x1", 0);
    integrator.addComputePerDof("v", "v+0.5*dt*f/m");
    integrator.addComputePerDof("x", "x+dt*v");
    integrator.addComputePerDof("x1", "x");
    integrator.addConstrainPositions();
    integrator.addComputePerDof("v", "v+0.5*dt*f/m+(x-x1)/dt");
    integrator.addConstrainVelocities();
    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);
    }
    
    // Constrain the first three particles with SHAKE.
    
    system.addConstraint(0, 1, 1.0);
    system.addConstraint(1, 2, 1.0);
    
    // Constrain the next three with SETTLE.
    
    system.addConstraint(3, 4, 1.0);
    system.addConstraint(5, 4, 1.0);
    system.addConstraint(3, 5, sqrt(2.0));
    
    // Constraint the rest with CCMA.
    
    for (int i = 6; 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) {
        integrator.step(2);
        State state = context.getState(State::Positions | State::Velocities | 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);
            if (i > 0) {
                Vec3 v1 = state.getVelocities()[particle1];
                Vec3 v2 = state.getVelocities()[particle2];
                double vel = (v1-v2).dot(p1-p2);
                ASSERT_EQUAL_TOL(0.0, vel, 2e-5);
            }
        }
        double energy = state.getKineticEnergy()+state.getPotentialEnergy();
        if (i == 0)
            initialEnergy = energy;
        else if (i > 0)
            ASSERT_EQUAL_TOL(initialEnergy, energy, 0.01);
    }
}

void testConstrainedMasslessParticles() {
    System system;
    system.addParticle(0.0);
    system.addParticle(1.0);
    system.addConstraint(0, 1, 1.5);
    vector<Vec3> positions(2);
    positions[0] = Vec3(-1, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    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");
    bool failed = false;
    try {
        // This should throw an exception.
        
        Context context(system, integrator, platform);
    }
    catch (exception& ex) {
        failed = true;
    }
    ASSERT(failed);
    
    // Now make both particles massless, which should work.
    
    system.setParticleMass(1, 0.0);
    Context context(system, integrator, platform);
    context.setPositions(positions);
    context.setVelocitiesToTemperature(300.0);
    integrator.step(1);
    State state = context.getState(State::Velocities | State::Positions);
    ASSERT_EQUAL(0.0, state.getVelocities()[0][0]);
}

/**
 * Test an integrator with an AndersenThermostat to see if updateContextState()
 * is being handled correctly.
 */
void testWithThermostat() {
    const int numParticles = 8;
    const double temp = 100.0;
    const double collisionFreq = 20.0;
    const int numSteps = 5000;
    System system;
    CustomIntegrator integrator(0.003);
    integrator.addUpdateContextState();
    integrator.addComputePerDof("v", "v+dt*f/m");
    integrator.addComputePerDof("x", "x+dt*v");
    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);
    integrator.setRandomNumberSeed(thermostat->getRandomNumberSeed());
    Context context(system, integrator, platform);
    vector<Vec3> positions(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));
    context.setPositions(positions);
    context.setVelocitiesToTemperature(temp);
    
    // Let it equilibrate.
    
    integrator.step(10000);
    
    // 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(10);
    }
    ke /= numSteps;
    double expected = 0.5*numParticles*3*BOLTZ*temp;
    ASSERT_USUALLY_EQUAL_TOL(expected, ke, 0.1);
}

/**
 * Test a Monte Carlo integrator that uses global variables and depends on energy.
 */
void testMonteCarlo() {
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    CustomIntegrator integrator(0.1);
    const double kT = BOLTZ*300.0;
    integrator.addGlobalVariable("kT", kT);
    integrator.addGlobalVariable("oldE", 0);
    integrator.addGlobalVariable("accept", 0);
    integrator.addPerDofVariable("oldx", 0);
    integrator.addComputeGlobal("oldE", "energy");
    integrator.addComputePerDof("oldx", "x");
    integrator.addComputePerDof("x", "x+dt*gaussian");
    integrator.addComputeGlobal("accept", "step(exp((oldE-energy)/kT)-uniform)");
    integrator.addComputePerDof("x", "accept*x + (1-accept)*oldx");
    HarmonicBondForce* forceField = new HarmonicBondForce();
    forceField->addBond(0, 1, 2.0, 10.0);
    system.addForce(forceField);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(-1, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    context.setPositions(positions);
    
    // Compute the histogram of distances and see if it satisfies a Boltzmann distribution.
    
    const int numBins = 100;
    const double maxDist = 4.0;
    const int numIterations = 5000;
    vector<int> counts(numBins, 0);
    for (int i = 0; i < numIterations; ++i) {
        integrator.step(10);
        State state = context.getState(State::Positions);
        Vec3 delta = state.getPositions()[0]-state.getPositions()[1];
        double dist = sqrt(delta.dot(delta));
        if (dist < maxDist)
            counts[(int) (numBins*dist/maxDist)]++;
    }
    vector<double> expected(numBins, 0);
    double sum = 0;
    for (int i = 0; i < numBins; i++) {
        double dist = (i+0.5)*maxDist/numBins;
        expected[i] = dist*dist*exp(-5.0*(dist-2)*(dist-2)/kT);
        sum += expected[i];
    }
    for (int i = 0; i < numBins; i++)
        ASSERT_USUALLY_EQUAL_TOL((double) counts[i]/numIterations, expected[i]/sum, 0.01);
}

/**
 * Test the ComputeSum operation.
 */
void testSum() {
    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);
    vector<Vec3> positions(numParticles);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    for (int i = 0; i < numParticles; i++) {
        system.addParticle(i%10 == 0 ? 0.0 : 1.5);
        nb->addParticle(i%2 == 0 ? 0.1 : -0.1, 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) < 1)
                    close = true;
            }
        }
    }
    CustomIntegrator integrator(0.005);
    integrator.addGlobalVariable("ke", 0);
    integrator.addComputePerDof("v", "v+dt*f/m");
    integrator.addComputePerDof("x", "x+dt*v");
    integrator.addComputeSum("ke", "m*v*v/2");
    Context context(system, integrator, platform);
    context.setPositions(positions);
    
    // See if the sum is being computed correctly.
    
    for (int i = 0; i < 100; ++i) {
        State state = context.getState(State::Energy);
        ASSERT_EQUAL_TOL(state.getKineticEnergy(), integrator.getGlobalVariable(0), 1e-5);
        integrator.step(1);
    }
}

/**
 * Test an integrator that both uses and modifies a context parameter.
 */
void testParameter() {
    System system;
    system.addParticle(1.0);
    AndersenThermostat* thermostat = new AndersenThermostat(0.1, 0.1);
    system.addForce(thermostat);
    CustomIntegrator integrator(0.1);
    integrator.addGlobalVariable("temp", 0);
    integrator.addComputeGlobal("temp", "AndersenTemperature");
    integrator.addComputeGlobal("AndersenTemperature", "temp*2");
    integrator.setRandomNumberSeed(thermostat->getRandomNumberSeed());
    Context context(system, integrator, platform);
    
    // See if the parameter is being used correctly.
    
    for (int i = 0; i < 10; i++) {
        integrator.step(1);
        ASSERT_EQUAL_TOL(context.getParameter("AndersenTemperature"), 0.1*(1<<(i+1)), 1e-5);
    }
}

/**
 * Test random number distributions.
 */
void testRandomDistributions() {
    const int numParticles = 100;
    const int numBins = 20;
    const int numSteps = 100;
    System system;
    for (int i = 0; i < numParticles; i++)
        system.addParticle(1.0);
    CustomIntegrator integrator(0.1);
    integrator.addPerDofVariable("a", 0);
    integrator.addPerDofVariable("b", 0);
    integrator.addComputePerDof("a", "uniform");
    integrator.addComputePerDof("b", "gaussian");
    Context context(system, integrator, platform);
    
    // See if the random numbers are distributed correctly.
    
    vector<int> bins(numBins);
    double mean = 0.0;
    double var = 0.0;
    double skew = 0.0;
    double kurtosis = 0.0;
    vector<Vec3> values;
    for (int i = 0; i < numSteps; i++) {
        integrator.step(1);
        integrator.getPerDofVariable(0, values);
        for (int i = 0; i < numParticles; i++)
            for (int j = 0; j < 3; j++) {
                double v = values[i][j];
                ASSERT(v >= 0 && v < 1);
                bins[(int) (v*numBins)]++;
            }
        integrator.getPerDofVariable(1, values);
        for (int i = 0; i < numParticles; i++)
            for (int j = 0; j < 3; j++) {
                double v = values[i][j];
                mean += v;
                var += v*v;
                skew += v*v*v;
                kurtosis += v*v*v*v;
            }
    }
    
    // Check the distribution of uniform randoms.
    
    int numValues = numParticles*numSteps*3;
    double expected = numValues/(double) numBins;
    double tol = 4*sqrt(expected);
    for (int i = 0; i < numBins; i++)
        ASSERT(bins[i] >= expected-tol && bins[i] <= expected+tol);
    
    // Check the distribution of gaussian randoms.
    
    mean /= numValues;
    var /= numValues;
    skew /= numValues;
    kurtosis /= numValues;
    double c2 = var-mean*mean;
    double c3 = skew-3*var*mean+2*mean*mean*mean;
    double c4 = kurtosis-4*skew*mean-3*var*var+12*var*mean*mean-6*mean*mean*mean*mean;
    ASSERT_EQUAL_TOL(0.0, mean, 3.0/sqrt((double) numValues));
    ASSERT_EQUAL_TOL(1.0, c2, 3.0/pow(numValues, 1.0/3.0));
    ASSERT_EQUAL_TOL(0.0, c3, 3.0/pow(numValues, 1.0/4.0));
    ASSERT_EQUAL_TOL(0.0, c4, 3.0/pow(numValues, 1.0/4.0));
}

/**
 * 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);
    }
}

/**
 * Test evaluating force groups separately.
 */
void testForceGroups() {
    System system;
    system.addParticle(2.0);
    system.addParticle(2.0);
    CustomIntegrator integrator(0.01);
    integrator.addPerDofVariable("outf", 0);
    integrator.addPerDofVariable("outf1", 0);
    integrator.addPerDofVariable("outf2", 0);
    integrator.addGlobalVariable("oute", 0);
    integrator.addGlobalVariable("oute1", 0);
    integrator.addGlobalVariable("oute2", 0);
    integrator.addComputePerDof("outf", "f");
    integrator.addComputePerDof("outf1", "f1");
    integrator.addComputePerDof("outf2", "f2");
    integrator.addComputeGlobal("oute", "energy");
    integrator.addComputeGlobal("oute1", "energy1");
    integrator.addComputeGlobal("oute2", "energy2");
    HarmonicBondForce* bonds = new HarmonicBondForce();
    bonds->addBond(0, 1, 1.5, 1.1);
    bonds->setForceGroup(1);
    system.addForce(bonds);
    NonbondedForce* nb = new NonbondedForce();
    nb->addParticle(0.2, 1, 0);
    nb->addParticle(0.2, 1, 0);
    nb->setForceGroup(2);
    system.addForce(nb);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(-1, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    context.setPositions(positions);
    
    // See if the various forces are computed correctly.
    
    integrator.step(1);
    vector<Vec3> f, f1, f2;
    double e1 = 0.5*1.1*0.5*0.5;
    double e2 = 138.935456*0.2*0.2/2.0;
    integrator.getPerDofVariable(0, f);
    integrator.getPerDofVariable(1, f1);
    integrator.getPerDofVariable(2, f2);
    ASSERT_EQUAL_VEC(Vec3(1.1*0.5, 0, 0), f1[0], 1e-5);
    ASSERT_EQUAL_VEC(Vec3(-1.1*0.5, 0, 0), f1[1], 1e-5);
    ASSERT_EQUAL_VEC(Vec3(-138.935456*0.2*0.2/4.0, 0, 0), f2[0], 1e-5);
    ASSERT_EQUAL_VEC(Vec3(138.935456*0.2*0.2/4.0, 0, 0), f2[1], 1e-5);
    ASSERT_EQUAL_VEC(f1[0]+f2[0], f[0], 1e-5);
    ASSERT_EQUAL_VEC(f1[1]+f2[1], f[1], 1e-5);
    ASSERT_EQUAL_TOL(e1, integrator.getGlobalVariable(1), 1e-5);
    ASSERT_EQUAL_TOL(e2, integrator.getGlobalVariable(2), 1e-5);
    ASSERT_EQUAL_TOL(e1+e2, integrator.getGlobalVariable(0), 1e-5);
    
    // Make sure they also match the values returned by the Context.
    
    State s = context.getState(State::Forces | State::Energy, false);
    State s1 = context.getState(State::Forces | State::Energy, false, 2);
    State s2 = context.getState(State::Forces | State::Energy, false, 4);
    vector<Vec3> c, c1, c2;
    c = context.getState(State::Forces, false).getForces();
    c1 = context.getState(State::Forces, false, 2).getForces();
    c2 = context.getState(State::Forces, false, 4).getForces();
    ASSERT_EQUAL_VEC(f[0], c[0], 1e-5);
    ASSERT_EQUAL_VEC(f[1], c[1], 1e-5);
    ASSERT_EQUAL_VEC(f1[0], c1[0], 1e-5);
    ASSERT_EQUAL_VEC(f1[1], c1[1], 1e-5);
    ASSERT_EQUAL_VEC(f2[0], c2[0], 1e-5);
    ASSERT_EQUAL_VEC(f2[1], c2[1], 1e-5);
    ASSERT_EQUAL_TOL(s.getPotentialEnergy(), integrator.getGlobalVariable(0), 1e-5);
    ASSERT_EQUAL_TOL(s1.getPotentialEnergy(), integrator.getGlobalVariable(1), 1e-5);
    ASSERT_EQUAL_TOL(s2.getPotentialEnergy(), integrator.getGlobalVariable(2), 1e-5);
}

/**
 * Test a multiple time step r-RESPA integrator.
 */
void testRespa() {
    const int numParticles = 8;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(4, 0, 0), Vec3(0, 4, 0), Vec3(0, 0, 4));
    CustomIntegrator integrator(0.002);
    integrator.addComputePerDof("v", "v+0.5*dt*f1/m");
    for (int i = 0; i < 2; i++) {
        integrator.addComputePerDof("v", "v+0.5*(dt/2)*f0/m");
        integrator.addComputePerDof("x", "x+(dt/2)*v");
        integrator.addComputePerDof("v", "v+0.5*(dt/2)*f0/m");
    }
    integrator.addComputePerDof("v", "v+0.5*dt*f1/m");
    HarmonicBondForce* bonds = new HarmonicBondForce();
    for (int i = 0; i < numParticles-2; i++)
        bonds->addBond(i, i+1, 1.0, 0.5);
    system.addForce(bonds);
    NonbondedForce* nb = new NonbondedForce();
    nb->setCutoffDistance(2.0);
    nb->setNonbondedMethod(NonbondedForce::Ewald);
    for (int i = 0; i < numParticles; ++i) {
        system.addParticle(i%2 == 0 ? 5.0 : 10.0);
        nb->addParticle((i%2 == 0 ? 0.2 : -0.2), 0.5, 5.0);
    }
    nb->setForceGroup(1);
    nb->setReciprocalSpaceForceGroup(0);
    system.addForce(nb);
    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 monitor energy conservations.
    
    double initialEnergy = 0.0;
    for (int i = 0; i < 1000; ++i) {
        State state = context.getState(State::Energy);
        double energy = state.getKineticEnergy()+state.getPotentialEnergy();
        if (i == 1)
            initialEnergy = energy;
        else if (i > 1)
            ASSERT_EQUAL_TOL(initialEnergy, energy, 0.05);
        integrator.step(2);
    }
}

/**
 * Make sure random numbers are computed correctly when steps get merged.
 */
void testMergedRandoms() {
    const int numParticles = 10;
    const int numSteps = 10;
    System system;
    for (int i = 0; i < numParticles; i++)
        system.addParticle(1.0);
    CustomIntegrator integrator(0.1);
    integrator.addPerDofVariable("dofUniform1", 0);
    integrator.addPerDofVariable("dofUniform2", 0);
    integrator.addPerDofVariable("dofGaussian1", 0);
    integrator.addPerDofVariable("dofGaussian2", 0);
    integrator.addGlobalVariable("globalUniform1", 0);
    integrator.addGlobalVariable("globalUniform2", 0);
    integrator.addGlobalVariable("globalGaussian1", 0);
    integrator.addGlobalVariable("globalGaussian2", 0);
    integrator.addComputePerDof("dofUniform1", "uniform");
    integrator.addComputePerDof("dofUniform2", "uniform");
    integrator.addComputePerDof("dofGaussian1", "gaussian");
    integrator.addComputePerDof("dofGaussian2", "gaussian");
    integrator.addComputeGlobal("globalUniform1", "uniform");
    integrator.addComputeGlobal("globalUniform2", "uniform");
    integrator.addComputeGlobal("globalGaussian1", "gaussian");
    integrator.addComputeGlobal("globalGaussian2", "gaussian");
    Context context(system, integrator, platform);
    
    // See if the random numbers are computed correctly.
    
    vector<Vec3> values1, values2;
    for (int i = 0; i < numSteps; i++) {
        integrator.step(1);
        integrator.getPerDofVariable(0, values1);
        integrator.getPerDofVariable(1, values2);
        for (int i = 0; i < numParticles; i++)
            for (int j = 0; j < 3; j++) {
                double v1 = values1[i][j];
                double v2 = values2[i][j];
                ASSERT(v1 >= 0 && v1 < 1);
                ASSERT(v2 >= 0 && v2 < 1);
                ASSERT(v1 != v2);
            }
        integrator.getPerDofVariable(2, values1);
        integrator.getPerDofVariable(3, values2);
        for (int i = 0; i < numParticles; i++)
            for (int j = 0; j < 3; j++) {
                double v1 = values1[i][j];
                double v2 = values2[i][j];
                ASSERT(v1 >= -10 && v1 < 10);
                ASSERT(v2 >= -10 && v2 < 10);
                ASSERT(v1 != v2);
            }
        double v1 = integrator.getGlobalVariable(0);
        double v2 = integrator.getGlobalVariable(1);
        ASSERT(v1 >= 0 && v1 < 1);
        ASSERT(v2 >= 0 && v2 < 1);
        ASSERT(v1 != v2);
        v1 = integrator.getGlobalVariable(2);
        v2 = integrator.getGlobalVariable(3);
        ASSERT(v1 >= -10 && v1 < 10);
        ASSERT(v2 >= -10 && v2 < 10);
        ASSERT(v1 != v2);
    }
}

int main(int argc, char* argv[]) {
    try {
        if (argc > 1)
            platform.setPropertyDefaultValue("CudaPrecision", string(argv[1]));
        testSingleBond();
        testConstraints();
        testVelocityConstraints();
        testConstrainedMasslessParticles();
        testWithThermostat();
        testMonteCarlo();
        testSum();
        testParameter();
        testRandomDistributions();
        testPerDofVariables();
        testForceGroups();
        testRespa();
        testMergedRandoms();
    }
    catch(const exception& e) {
        cout << "exception: " << e.what() << endl;
        return 1;
    }
    cout << "Done" << endl;
    return 0;
}