void CudaIntegrateRPMDStepKernel::computeForces(ContextImpl& context) {
    // Compute forces from all groups that didn't have a specified contraction.

    for (int i = 0; i < numCopies; i++) {
        void* copyToContextArgs[] = {&velocities->getDevicePointer(), &cu.getVelm().getDevicePointer(), &positions->getDevicePointer(),
                &cu.getPosq().getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(), &i};
        cu.executeKernel(copyToContextKernel, copyToContextArgs, cu.getNumAtoms());
        context.computeVirtualSites();
        Vec3 initialBox[3];
        context.getPeriodicBoxVectors(initialBox[0], initialBox[1], initialBox[2]);
        context.updateContextState();
        Vec3 finalBox[3];
        context.getPeriodicBoxVectors(finalBox[0], finalBox[1], finalBox[2]);
        if (initialBox[0] != finalBox[0] || initialBox[1] != finalBox[1] || initialBox[2] != finalBox[2])
            throw OpenMMException("Standard barostats cannot be used with RPMDIntegrator.  Use RPMDMonteCarloBarostat instead.");
        context.calcForcesAndEnergy(true, false, groupsNotContracted);
        void* copyFromContextArgs[] = {&cu.getForce().getDevicePointer(), &forces->getDevicePointer(), &cu.getVelm().getDevicePointer(),
                &velocities->getDevicePointer(), &cu.getPosq().getDevicePointer(), &positions->getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(), &i};
        cu.executeKernel(copyFromContextKernel, copyFromContextArgs, cu.getNumAtoms());
    }
    
    // Now loop over contractions and compute forces from them.
    
    for (map<int, int>::const_iterator iter = groupsByCopies.begin(); iter != groupsByCopies.end(); ++iter) {
        int copies = iter->first;
        int groupFlags = iter->second;
        
        // Find the contracted positions.
        
        void* contractPosArgs[] = {&positions->getDevicePointer(), &contractedPositions->getDevicePointer()};
        cu.executeKernel(positionContractionKernels[copies], contractPosArgs, numParticles*numCopies, workgroupSize);

        // Compute forces.

        for (int i = 0; i < copies; i++) {
            void* copyToContextArgs[] = {&velocities->getDevicePointer(), &cu.getVelm().getDevicePointer(), &contractedPositions->getDevicePointer(),
                    &cu.getPosq().getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(), &i};
            cu.executeKernel(copyToContextKernel, copyToContextArgs, cu.getNumAtoms());
            context.computeVirtualSites();
            context.calcForcesAndEnergy(true, false, groupFlags);
            void* copyFromContextArgs[] = {&cu.getForce().getDevicePointer(), &contractedForces->getDevicePointer(), &cu.getVelm().getDevicePointer(),
                   &velocities->getDevicePointer(), &cu.getPosq().getDevicePointer(), &contractedPositions->getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(), &i};
            cu.executeKernel(copyFromContextKernel, copyFromContextArgs, cu.getNumAtoms());
        }
        
        // Apply the forces to the original copies.
        
        void* contractForceArgs[] = {&forces->getDevicePointer(), &contractedForces->getDevicePointer()};
        cu.executeKernel(forceContractionKernels[copies], contractForceArgs, numParticles*numCopies, workgroupSize);
    }
    if (groupsByCopies.size() > 0) {
        // Ensure the Context contains the positions from the last copy, since we'll assume that later.
        
        int i = numCopies-1;
        void* copyToContextArgs[] = {&velocities->getDevicePointer(), &cu.getVelm().getDevicePointer(), &positions->getDevicePointer(),
                &cu.getPosq().getDevicePointer(), &cu.getAtomIndexArray().getDevicePointer(), &i};
        cu.executeKernel(copyToContextKernel, copyToContextArgs, cu.getNumAtoms());
    }
}
void ReferenceCustomDynamics::update(ContextImpl& context, int numberOfAtoms, vector<RealVec>& atomCoordinates,
                                     vector<RealVec>& velocities, vector<RealVec>& forces, vector<RealOpenMM>& masses,
                                     map<string, RealOpenMM>& globals, vector<vector<RealVec> >& perDof, bool& forcesAreValid, RealOpenMM tolerance) {
    if (invalidatesForces.size() == 0)
        initialize(context, masses, globals);
    int numSteps = stepType.size();
    globals.insert(context.getParameters().begin(), context.getParameters().end());
    for (map<string, RealOpenMM>::const_iterator iter = globals.begin(); iter != globals.end(); ++iter)
        expressionSet.setVariable(expressionSet.getVariableIndex(iter->first), iter->second);
    oldPos = atomCoordinates;
    
    // Loop over steps and execute them.
    
    for (int step = 0; step < numSteps; ) {
        if ((needsForces[step] || needsEnergy[step]) && (!forcesAreValid || context.getLastForceGroups() != forceGroupFlags[step])) {
            // Recompute forces and/or energy.
            
            bool computeForce = needsForces[step] || computeBothForceAndEnergy[step];
            bool computeEnergy = needsEnergy[step] || computeBothForceAndEnergy[step];
            recordChangedParameters(context, globals);
            RealOpenMM e = context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroupFlags[step]);
            if (computeEnergy) {
                energy = e;
                context.getEnergyParameterDerivatives(energyParamDerivs);
            }
            forcesAreValid = true;
        }
        
        // Execute the step.

        int nextStep = step+1;
        switch (stepType[step]) {
            case CustomIntegrator::ComputeGlobal: {
                uniform = SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber();
                gaussian = SimTKOpenMMUtilities::getNormallyDistributedRandomNumber();
                RealOpenMM result = stepExpressions[step][0].evaluate();
                globals[stepVariable[step]] = result;
                expressionSet.setVariable(stepVariableIndex[step], result);
                break;
            }
            case CustomIntegrator::ComputePerDof: {
                vector<RealVec>* results = NULL;
                if (stepVariableIndex[step] == xIndex)
                    results = &atomCoordinates;
                else if (stepVariableIndex[step] == vIndex)
                    results = &velocities;
                else {
                    for (int j = 0; j < integrator.getNumPerDofVariables(); j++)
                        if (stepVariableIndex[step] == perDofVariableIndex[j])
                            results = &perDof[j];
                }
                if (results == NULL)
                    throw OpenMMException("Illegal per-DOF output variable: "+stepVariable[step]);
                computePerDof(numberOfAtoms, *results, atomCoordinates, velocities, forces, masses, perDof, stepExpressions[step][0]);
                break;
            }
            case CustomIntegrator::ComputeSum: {
                computePerDof(numberOfAtoms, sumBuffer, atomCoordinates, velocities, forces, masses, perDof, stepExpressions[step][0]);
                RealOpenMM sum = 0.0;
                for (int j = 0; j < numberOfAtoms; j++)
                    if (masses[j] != 0.0)
                        sum += sumBuffer[j][0]+sumBuffer[j][1]+sumBuffer[j][2];
                globals[stepVariable[step]] = sum;
                expressionSet.setVariable(stepVariableIndex[step], sum);
                break;
            }
            case CustomIntegrator::ConstrainPositions: {
                getReferenceConstraintAlgorithm()->apply(oldPos, atomCoordinates, inverseMasses, tolerance);
                oldPos = atomCoordinates;
                break;
            }
            case CustomIntegrator::ConstrainVelocities: {
                getReferenceConstraintAlgorithm()->applyToVelocities(oldPos, velocities, inverseMasses, tolerance);
                break;
            }
            case CustomIntegrator::UpdateContextState: {
                recordChangedParameters(context, globals);
                context.updateContextState();
                globals.insert(context.getParameters().begin(), context.getParameters().end());
                for (map<string, RealOpenMM>::const_iterator iter = globals.begin(); iter != globals.end(); ++iter)
                    expressionSet.setVariable(expressionSet.getVariableIndex(iter->first), iter->second);
                break;
            }
            case CustomIntegrator::IfBlockStart: {
                if (!evaluateCondition(step))
                    nextStep = blockEnd[step]+1;
                break;
            }
            case CustomIntegrator::WhileBlockStart: {
                if (!evaluateCondition(step))
                    nextStep = blockEnd[step]+1;
                break;
            }
            case CustomIntegrator::BlockEnd: {
                if (blockEnd[step] != -1)
                    nextStep = blockEnd[step]; // Return to the start of a while block.
                break;
            }
        }
        if (invalidatesForces[step])
            forcesAreValid = false;
        step = nextStep;
    }
    ReferenceVirtualSites::computePositions(context.getSystem(), atomCoordinates);
    incrementTimeStep();
    recordChangedParameters(context, globals);
}
예제 #3
0
void ReferenceCustomDynamics::update(ContextImpl& context, int numberOfAtoms, vector<RealVec>& atomCoordinates,
                                     vector<RealVec>& velocities, vector<RealVec>& forces, vector<RealOpenMM>& masses,
                                     map<string, RealOpenMM>& globals, vector<vector<RealVec> >& perDof, bool& forcesAreValid, RealOpenMM tolerance) {
    int numSteps = stepType.size();
    globals.insert(context.getParameters().begin(), context.getParameters().end());
    oldPos = atomCoordinates;
    if (invalidatesForces.size() == 0) {
        // Some initialization can't be done in the constructor, since we need a ContextImpl from which to get the list of
        // Context parameters.  Instead, we do it the first time this method is called.

        vector<int> forceGroup;
        vector<vector<Lepton::ParsedExpression> > expressions;
        CustomIntegratorUtilities::analyzeComputations(context, integrator, expressions, comparisons, blockEnd, invalidatesForces, needsForces, needsEnergy, computeBothForceAndEnergy, forceGroup);
        stepExpressions.resize(expressions.size());
        for (int i = 0; i < numSteps; i++) {
            for (int j = 0; j < (int) expressions[i].size(); j++)
                stepExpressions[i].push_back(expressions[i][j].createProgram());
            if (stepType[i] == CustomIntegrator::BeginWhileBlock)
                blockEnd[blockEnd[i]] = i; // Record where to branch back to.
        }

        // Record the variable names and flags for the force and energy in each step.

        forceGroupFlags.resize(numSteps, -1);
        forceName.resize(numSteps, "f");
        energyName.resize(numSteps, "energy");
        vector<string> forceGroupName;
        vector<string> energyGroupName;
        for (int i = 0; i < 32; i++) {
            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
        }
        for (int i = 0; i < numSteps; i++) {
            if (needsForces[i] && forceGroup[i] > -1)
                forceName[i] = forceGroupName[forceGroup[i]];
            if (needsEnergy[i] && forceGroup[i] > -1)
                energyName[i] = energyGroupName[forceGroup[i]];
            if (forceGroup[i] > -1)
                forceGroupFlags[i] = 1<<forceGroup[i];
        }
        
        // Build the list of inverse masses.
        
        inverseMasses.resize(numberOfAtoms);
        for (int i = 0; i < numberOfAtoms; i++) {
            if (masses[i] == 0.0)
                inverseMasses[i] = 0.0;
            else
                inverseMasses[i] = 1.0/masses[i];
        }
    }
    
    // Loop over steps and execute them.
    
    for (int step = 0; step < numSteps; ) {
        if ((needsForces[step] || needsEnergy[step]) && (!forcesAreValid || context.getLastForceGroups() != forceGroupFlags[step])) {
            // Recompute forces and/or energy.
            
            bool computeForce = needsForces[step] || computeBothForceAndEnergy[step];
            bool computeEnergy = needsEnergy[step] || computeBothForceAndEnergy[step];
            recordChangedParameters(context, globals);
            RealOpenMM e = context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroupFlags[step]);
            if (computeEnergy)
                energy = e;
            forcesAreValid = true;
        }
        globals[energyName[step]] = energy;
        
        // Execute the step.

        int nextStep = step+1;
        switch (stepType[step]) {
            case CustomIntegrator::ComputeGlobal: {
                map<string, RealOpenMM> variables = globals;
                variables["uniform"] = SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber();
                variables["gaussian"] = SimTKOpenMMUtilities::getNormallyDistributedRandomNumber();
                globals[stepVariable[step]] = stepExpressions[step][0].evaluate(variables);
                break;
            }
            case CustomIntegrator::ComputePerDof: {
                vector<RealVec>* results = NULL;
                if (stepVariable[step] == "x")
                    results = &atomCoordinates;
                else if (stepVariable[step] == "v")
                    results = &velocities;
                else {
                    for (int j = 0; j < integrator.getNumPerDofVariables(); j++)
                        if (stepVariable[step] == integrator.getPerDofVariableName(j))
                            results = &perDof[j];
                }
                if (results == NULL)
                    throw OpenMMException("Illegal per-DOF output variable: "+stepVariable[step]);
                computePerDof(numberOfAtoms, *results, atomCoordinates, velocities, forces, masses, globals, perDof, stepExpressions[step][0], forceName[step]);
                break;
            }
            case CustomIntegrator::ComputeSum: {
                computePerDof(numberOfAtoms, sumBuffer, atomCoordinates, velocities, forces, masses, globals, perDof, stepExpressions[step][0], forceName[step]);
                RealOpenMM sum = 0.0;
                for (int j = 0; j < numberOfAtoms; j++)
                    if (masses[j] != 0.0)
                        sum += sumBuffer[j][0]+sumBuffer[j][1]+sumBuffer[j][2];
                globals[stepVariable[step]] = sum;
                break;
            }
            case CustomIntegrator::ConstrainPositions: {
                getReferenceConstraintAlgorithm()->apply(oldPos, atomCoordinates, inverseMasses, tolerance);
                oldPos = atomCoordinates;
                break;
            }
            case CustomIntegrator::ConstrainVelocities: {
                getReferenceConstraintAlgorithm()->applyToVelocities(oldPos, velocities, inverseMasses, tolerance);
                break;
            }
            case CustomIntegrator::UpdateContextState: {
                recordChangedParameters(context, globals);
                context.updateContextState();
                globals.insert(context.getParameters().begin(), context.getParameters().end());
                break;
            }
            case CustomIntegrator::BeginIfBlock: {
                if (!evaluateCondition(step, globals))
                    nextStep = blockEnd[step]+1;
                break;
            }
            case CustomIntegrator::BeginWhileBlock: {
                if (!evaluateCondition(step, globals))
                    nextStep = blockEnd[step]+1;
                break;
            }
            case CustomIntegrator::EndBlock: {
                if (blockEnd[step] != -1)
                    nextStep = blockEnd[step]; // Return to the start of a while block.
                break;
            }
        }
        if (invalidatesForces[step])
            forcesAreValid = false;
        step = nextStep;
    }
    ReferenceVirtualSites::computePositions(context.getSystem(), atomCoordinates);
    incrementTimeStep();
    recordChangedParameters(context, globals);
}
예제 #4
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void ReferenceCustomDynamics::update(ContextImpl& context, int numberOfAtoms, vector<RealVec>& atomCoordinates,
                                     vector<RealVec>& velocities, vector<RealVec>& forces, vector<RealOpenMM>& masses,
                                     map<string, RealOpenMM>& globals, vector<vector<RealVec> >& perDof, bool& forcesAreValid, RealOpenMM tolerance){
    int numSteps = stepType.size();
    globals.insert(context.getParameters().begin(), context.getParameters().end());
    oldPos = atomCoordinates;
    if (invalidatesForces.size() == 0) {
        // The first time this is called, work out when to recompute forces and energy.  First build a
        // list of every step that invalidates the forces.
        
        invalidatesForces.resize(numSteps, false);
        needsForces.resize(numSteps, false);
        needsEnergy.resize(numSteps, false);
        forceGroup.resize(numSteps, -2);
        forceName.resize(numSteps, "f");
        energyName.resize(numSteps, "energy");
        set<string> affectsForce;
        affectsForce.insert("x");
        for (vector<ForceImpl*>::const_iterator iter = context.getForceImpls().begin(); iter != context.getForceImpls().end(); ++iter) {
            const map<string, double> params = (*iter)->getDefaultParameters();
            for (map<string, double>::const_iterator param = params.begin(); param != params.end(); ++param)
                affectsForce.insert(param->first);
        }
        for (int i = 0; i < numSteps; i++)
            invalidatesForces[i] = (stepType[i] == CustomIntegrator::ConstrainPositions || affectsForce.find(stepVariable[i]) != affectsForce.end());
        
        // Make a list of which steps require valid forces or energy to be known.
        
        vector<string> forceGroupName;
        vector<string> energyGroupName;
        for (int i = 0; i < 32; i++) {
            stringstream fname;
            fname << "f" << i;
            forceGroupName.push_back(fname.str());
            stringstream ename;
            ename << "energy" << i;
            energyGroupName.push_back(ename.str());
        }
        for (int i = 0; i < numSteps; i++) {
            if (stepType[i] == CustomIntegrator::ComputeGlobal || stepType[i] == CustomIntegrator::ComputePerDof || stepType[i] == CustomIntegrator::ComputeSum) {
                for (int j = 0; j < stepExpression[i].getNumOperations(); j++) {
                    const Lepton::Operation& op = stepExpression[i].getOperation(j);
                    if (op.getId() == Lepton::Operation::VARIABLE) {
                        if (op.getName() == "energy") {
                            if (forceGroup[i] != -2)
                                throw OpenMMException("A single computation step cannot depend on multiple force groups");
                            needsEnergy[i] = true;
                            forceGroup[i] = -1;
                        }
                        else if (op.getName().substr(0, 6) == "energy") {
                            for (int k = 0; k < (int) energyGroupName.size(); k++)
                                if (op.getName() == energyGroupName[k]) {
                                    if (forceGroup[i] != -2)
                                        throw OpenMMException("A single computation step cannot depend on multiple force groups");
                                    needsForces[i] = true;
                                    forceGroup[i] = 1<<k;
                                    energyName[i] = energyGroupName[k];
                                    break;
                                }
                        }
                        else if (op.getName() == "f") {
                            if (forceGroup[i] != -2)
                                throw OpenMMException("A single computation step cannot depend on multiple force groups");
                            needsForces[i] = true;
                            forceGroup[i] = -1;
                        }
                        else if (op.getName()[0] == 'f') {
                            for (int k = 0; k < (int) forceGroupName.size(); k++)
                                if (op.getName() == forceGroupName[k]) {
                                    if (forceGroup[i] != -2)
                                        throw OpenMMException("A single computation step cannot depend on multiple force groups");
                                    needsForces[i] = true;
                                    forceGroup[i] = 1<<k;
                                    forceName[i] = forceGroupName[k];
                                    break;
                                }
                        }
                    }
                }
            }
        }
        
        // Build the list of inverse masses.
        
        inverseMasses.resize(numberOfAtoms);
        for (int i = 0; i < numberOfAtoms; i++) {
            if (masses[i] == 0.0)
                inverseMasses[i] = 0.0;
            else
                inverseMasses[i] = 1.0/masses[i];
        }
    }
    
    // Loop over steps and execute them.
    
    for (int i = 0; i < numSteps; i++) {
        if ((needsForces[i] || needsEnergy[i]) && (!forcesAreValid || context.getLastForceGroups() != forceGroup[i])) {
            // Recompute forces and or energy.  Figure out what is actually needed
            // between now and the next time they get invalidated again.
            
            bool computeForce = false, computeEnergy = false;
            for (int j = i; ; j++) {
                if (needsForces[j])
                    computeForce = true;
                if (needsEnergy[j])
                    computeEnergy = true;
                if (invalidatesForces[j])
                    break;
                if (j == numSteps-1)
                    j = -1;
                if (j == i-1)
                    break;
            }
            recordChangedParameters(context, globals);
            RealOpenMM e = context.calcForcesAndEnergy(computeForce, computeEnergy, forceGroup[i]);
            if (computeEnergy)
                energy = e;
            forcesAreValid = true;
        }
        globals[energyName[i]] = energy;
        
        // Execute the step.
        
        switch (stepType[i]) {
            case CustomIntegrator::ComputeGlobal: {
                map<string, RealOpenMM> variables = globals;
                variables["uniform"] = SimTKOpenMMUtilities::getUniformlyDistributedRandomNumber();
                variables["gaussian"] = SimTKOpenMMUtilities::getNormallyDistributedRandomNumber();
                globals[stepVariable[i]] = stepExpression[i].evaluate(variables);
                break;
            }
            case CustomIntegrator::ComputePerDof: {
                vector<RealVec>* results = NULL;
                if (stepVariable[i] == "x")
                    results = &atomCoordinates;
                else if (stepVariable[i] == "v")
                    results = &velocities;
                else {
                    for (int j = 0; j < integrator.getNumPerDofVariables(); j++)
                        if (stepVariable[i] == integrator.getPerDofVariableName(j))
                            results = &perDof[j];
                }
                if (results == NULL)
                    throw OpenMMException("Illegal per-DOF output variable: "+stepVariable[i]);
                computePerDof(numberOfAtoms, *results, atomCoordinates, velocities, forces, masses, globals, perDof, stepExpression[i], forceName[i]);
                break;
            }
            case CustomIntegrator::ComputeSum: {
                computePerDof(numberOfAtoms, sumBuffer, atomCoordinates, velocities, forces, masses, globals, perDof, stepExpression[i], forceName[i]);
                RealOpenMM sum = 0.0;
                for (int j = 0; j < numberOfAtoms; j++)
                    if (masses[j] != 0.0)
                        sum += sumBuffer[j][0]+sumBuffer[j][1]+sumBuffer[j][2];
                globals[stepVariable[i]] = sum;
                break;
            }
            case CustomIntegrator::ConstrainPositions: {
                getReferenceConstraintAlgorithm()->apply(oldPos, atomCoordinates, inverseMasses, tolerance);
                oldPos = atomCoordinates;
                break;
            }
            case CustomIntegrator::ConstrainVelocities: {
                getReferenceConstraintAlgorithm()->applyToVelocities(oldPos, velocities, inverseMasses, tolerance);
                break;
            }
            case CustomIntegrator::UpdateContextState: {
                recordChangedParameters(context, globals);
                context.updateContextState();
                globals.insert(context.getParameters().begin(), context.getParameters().end());
            }
        }
        if (invalidatesForces[i])
            forcesAreValid = false;
    }
    ReferenceVirtualSites::computePositions(context.getSystem(), atomCoordinates);
    incrementTimeStep();
    recordChangedParameters(context, globals);
}
예제 #5
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void ReferenceIntegrateRPMDStepKernel::computeForces(ContextImpl& context, const RPMDIntegrator& integrator) {
    const int totalCopies = positions.size();
    const int numParticles = positions[0].size();
    vector<RealVec>& pos = extractPositions(context);
    vector<RealVec>& vel = extractVelocities(context);
    vector<RealVec>& f = extractForces(context);
    
    // Compute forces from all groups that didn't have a specified contraction.
    
    for (int i = 0; i < totalCopies; i++) {
        pos = positions[i];
        vel = velocities[i];
        context.computeVirtualSites();
        Vec3 initialBox[3];
        context.getPeriodicBoxVectors(initialBox[0], initialBox[1], initialBox[2]);
        context.updateContextState();
        Vec3 finalBox[3];
        context.getPeriodicBoxVectors(finalBox[0], finalBox[1], finalBox[2]);
        if (initialBox[0] != finalBox[0] || initialBox[1] != finalBox[1] || initialBox[2] != finalBox[2]) {
            // A barostat was applied during updateContextState().  Adjust the particle positions in all the
            // other copies to match this one.
            
            for (int j = 0; j < numParticles; j++) {
                Vec3 delta = pos[j]-positions[i][j];
                for (int k = 0; k < totalCopies; k++)
                    if (k != i)
                        positions[k][j] += delta;
            }
        }
        positions[i] = pos;
        velocities[i] = vel;
        context.calcForcesAndEnergy(true, false, groupsNotContracted);
        forces[i] = f;
    }
    
    // Now loop over contractions and compute forces from them.
    
    for (map<int, int>::const_iterator iter = groupsByCopies.begin(); iter != groupsByCopies.end(); ++iter) {
        int copies = iter->first;
        int groupFlags = iter->second;
        fftpack* shortFFT = contractionFFT[copies];
        
        // Find the contracted positions.
        
        vector<t_complex> q(totalCopies);
        const RealOpenMM scale1 = 1.0/totalCopies;
        for (int particle = 0; particle < numParticles; particle++) {
            for (int component = 0; component < 3; component++) {
                // Transform to the frequency domain, set high frequency components to zero, and transform back.
                
                for (int k = 0; k < totalCopies; k++)
                    q[k] = t_complex(positions[k][particle][component], 0.0);
                fftpack_exec_1d(fft, FFTPACK_FORWARD, &q[0], &q[0]);
                if (copies > 1) {
                    int start = (copies+1)/2;
                    int end = totalCopies-copies+start;
                    for (int k = end; k < totalCopies; k++)
                        q[k-(totalCopies-copies)] = q[k];
                    fftpack_exec_1d(shortFFT, FFTPACK_BACKWARD, &q[0], &q[0]);
                }
                for (int k = 0; k < copies; k++)
                    contractedPositions[k][particle][component] = scale1*q[k].re;
            }
        }
        
        // Compute forces.

        for (int i = 0; i < copies; i++) {
            pos = contractedPositions[i];
            context.computeVirtualSites();
            context.calcForcesAndEnergy(true, false, groupFlags);
            contractedForces[i] = f;
        }
        
        // Apply the forces to the original copies.
        
        const RealOpenMM scale2 = 1.0/copies;
        for (int particle = 0; particle < numParticles; particle++) {
            for (int component = 0; component < 3; component++) {
                // Transform to the frequency domain, pad with zeros, and transform back.
                
                for (int k = 0; k < copies; k++)
                    q[k] = t_complex(contractedForces[k][particle][component], 0.0);
                if (copies > 1)
                    fftpack_exec_1d(shortFFT, FFTPACK_FORWARD, &q[0], &q[0]);
                int start = (copies+1)/2;
                int end = totalCopies-copies+start;
                for (int k = end; k < totalCopies; k++)
                    q[k] = q[k-(totalCopies-copies)];
                for (int k = start; k < end; k++)
                    q[k] = t_complex(0, 0);
                fftpack_exec_1d(fft, FFTPACK_BACKWARD, &q[0], &q[0]);
                for (int k = 0; k < totalCopies; k++)
                    forces[k][particle][component] += scale2*q[k].re;
            }
        }
    }
}