Virtual sites can depend on other virtual sites (#4348)

* Reference platform supports nested virtual sites

* Common platform supports nested virtual sites

* Fixed force distribution from nested virtual sites

* Fixed test failures

platforms/reference/src/SimTKReference/ReferenceVerletDynamics.cpp

@@ -114,6 +114,6 @@ void ReferenceVerletDynamics::update(const OpenMM::System& system, vector<Vec3>&
            }
    }
 
-   ReferenceVirtualSites::computePositions(system, atomCoordinates);
+   getVirtualSites().computePositions(system, atomCoordinates);
    incrementTimeStep();
 }

platforms/reference/src/SimTKReference/ReferenceVirtualSites.cpp

@@ -31,163 +31,189 @@
 
 #include "ReferenceVirtualSites.h"
 #include "openmm/VirtualSite.h"
+#include "openmm/OpenMMException.h"
 #include <cmath>
+#include <set>
 
 using namespace OpenMM;
 using namespace std;
 
-void ReferenceVirtualSites::computePositions(const OpenMM::System& system, vector<OpenMM::Vec3>& atomCoordinates) {
+ReferenceVirtualSites::ReferenceVirtualSites(const System& system) {
+    set<int> sites;
     for (int i = 0; i < system.getNumParticles(); i++)
-        if (system.isVirtualSite(i)) {
-            if (dynamic_cast<const TwoParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A two particle average.
-                
-                const TwoParticleAverageSite& site = dynamic_cast<const TwoParticleAverageSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1);
-                double w1 = site.getWeight(0), w2 = site.getWeight(1);
-                atomCoordinates[i] = atomCoordinates[p1]*w1 + atomCoordinates[p2]*w2;
-            }
-            else if (dynamic_cast<const ThreeParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A three particle average.
-                
-                const ThreeParticleAverageSite& site = dynamic_cast<const ThreeParticleAverageSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
-                double w1 = site.getWeight(0), w2 = site.getWeight(1), w3 = site.getWeight(2);
-                atomCoordinates[i] = atomCoordinates[p1]*w1 + atomCoordinates[p2]*w2 + atomCoordinates[p3]*w3;
-            }
-            else if (dynamic_cast<const OutOfPlaneSite*>(&system.getVirtualSite(i)) != NULL) {
-                // An out of plane site.
-                
-                const OutOfPlaneSite& site = dynamic_cast<const OutOfPlaneSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
-                double w12 = site.getWeight12(), w13 = site.getWeight13(), wcross = site.getWeightCross();
-                Vec3 v12 = atomCoordinates[p2]-atomCoordinates[p1];
-                Vec3 v13 = atomCoordinates[p3]-atomCoordinates[p1];
-                Vec3 cross = v12.cross(v13);
-                atomCoordinates[i] = atomCoordinates[p1] + v12*w12 + v13*w13 + cross*wcross;
-            }
-            else if (dynamic_cast<const LocalCoordinatesSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A local coordinates site.
-                
-                const LocalCoordinatesSite& site = dynamic_cast<const LocalCoordinatesSite&>(system.getVirtualSite(i));
-                int numParticles = site.getNumParticles();
-                vector<double> originWeights, xWeights, yWeights;
-                site.getOriginWeights(originWeights);
-                site.getXWeights(xWeights);
-                site.getYWeights(yWeights);
-                Vec3 origin, xdir, ydir;
-                for (int j = 0; j < numParticles; j++) {
-                    Vec3 pos = atomCoordinates[site.getParticle(j)];
-                    origin += pos*originWeights[j];
-                    xdir += pos*xWeights[j];
-                    ydir += pos*yWeights[j];
-                }
-                Vec3 localPosition = site.getLocalPosition();
-                Vec3 zdir = xdir.cross(ydir);
-                double normXdir = sqrt(xdir.dot(xdir));
-                double normZdir = sqrt(zdir.dot(zdir));
-                if (normXdir > 0.0)
-                    xdir /= normXdir;
-                if (normZdir > 0.0)
-                    zdir /= normZdir;
-                ydir = zdir.cross(xdir);
-                atomCoordinates[i] = origin + xdir*localPosition[0] + ydir*localPosition[1] + zdir*localPosition[2];
+        if (system.isVirtualSite(i))
+            sites.insert(i);
+    int remainingSites = 0;
+    while (sites.size() > 0) {
+        if (sites.size() == remainingSites)
+            throw OpenMMException("Virtual site definitions are circular");
+        for (auto index = sites.begin(); index != sites.end();) {
+            const VirtualSite& site = system.getVirtualSite(*index);
+            bool canCompute = true;
+            for (int i = 0; i < site.getNumParticles(); i++)
+                if (sites.find(site.getParticle(i)) != sites.end())
+                    canCompute = false;
+            if (canCompute) {
+                order.push_back(*index);
+                index = sites.erase(index);
             }
+            else
+                ++index;
         }
+    }
 }
 
-void ReferenceVirtualSites::distributeForces(const OpenMM::System& system, const vector<OpenMM::Vec3>& atomCoordinates, vector<OpenMM::Vec3>& forces) {
-    for (int i = 0; i < system.getNumParticles(); i++)
-        if (system.isVirtualSite(i)) {
-            Vec3 f = forces[i];
-            if (dynamic_cast<const TwoParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A two particle average.
-                
-                const TwoParticleAverageSite& site = dynamic_cast<const TwoParticleAverageSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1);
-                double w1 = site.getWeight(0), w2 = site.getWeight(1);
-                forces[p1] += f*w1;
-                forces[p2] += f*w2;
+void ReferenceVirtualSites::computePositions(const OpenMM::System& system, vector<OpenMM::Vec3>& atomCoordinates) const {
+    for (int i : order) {
+        if (dynamic_cast<const TwoParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A two particle average.
+
+            const TwoParticleAverageSite& site = dynamic_cast<const TwoParticleAverageSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1);
+            double w1 = site.getWeight(0), w2 = site.getWeight(1);
+            atomCoordinates[i] = atomCoordinates[p1]*w1 + atomCoordinates[p2]*w2;
+        }
+        else if (dynamic_cast<const ThreeParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A three particle average.
+
+            const ThreeParticleAverageSite& site = dynamic_cast<const ThreeParticleAverageSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
+            double w1 = site.getWeight(0), w2 = site.getWeight(1), w3 = site.getWeight(2);
+            atomCoordinates[i] = atomCoordinates[p1]*w1 + atomCoordinates[p2]*w2 + atomCoordinates[p3]*w3;
+        }
+        else if (dynamic_cast<const OutOfPlaneSite*>(&system.getVirtualSite(i)) != NULL) {
+            // An out of plane site.
+
+            const OutOfPlaneSite& site = dynamic_cast<const OutOfPlaneSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
+            double w12 = site.getWeight12(), w13 = site.getWeight13(), wcross = site.getWeightCross();
+            Vec3 v12 = atomCoordinates[p2]-atomCoordinates[p1];
+            Vec3 v13 = atomCoordinates[p3]-atomCoordinates[p1];
+            Vec3 cross = v12.cross(v13);
+            atomCoordinates[i] = atomCoordinates[p1] + v12*w12 + v13*w13 + cross*wcross;
+        }
+        else if (dynamic_cast<const LocalCoordinatesSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A local coordinates site.
+
+            const LocalCoordinatesSite& site = dynamic_cast<const LocalCoordinatesSite&>(system.getVirtualSite(i));
+            int numParticles = site.getNumParticles();
+            vector<double> originWeights, xWeights, yWeights;
+            site.getOriginWeights(originWeights);
+            site.getXWeights(xWeights);
+            site.getYWeights(yWeights);
+            Vec3 origin, xdir, ydir;
+            for (int j = 0; j < numParticles; j++) {
+                Vec3 pos = atomCoordinates[site.getParticle(j)];
+                origin += pos*originWeights[j];
+                xdir += pos*xWeights[j];
+                ydir += pos*yWeights[j];
             }
-            else if (dynamic_cast<const ThreeParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A three particle average.
-                
-                const ThreeParticleAverageSite& site = dynamic_cast<const ThreeParticleAverageSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
-                double w1 = site.getWeight(0), w2 = site.getWeight(1), w3 = site.getWeight(2);
-                forces[p1] += f*w1;
-                forces[p2] += f*w2;
-                forces[p3] += f*w3;
+            Vec3 localPosition = site.getLocalPosition();
+            Vec3 zdir = xdir.cross(ydir);
+            double normXdir = sqrt(xdir.dot(xdir));
+            double normZdir = sqrt(zdir.dot(zdir));
+            if (normXdir > 0.0)
+                xdir /= normXdir;
+            if (normZdir > 0.0)
+                zdir /= normZdir;
+            ydir = zdir.cross(xdir);
+            atomCoordinates[i] = origin + xdir*localPosition[0] + ydir*localPosition[1] + zdir*localPosition[2];
+        }
+    }
+}
+
+void ReferenceVirtualSites::distributeForces(const OpenMM::System& system, const vector<OpenMM::Vec3>& atomCoordinates, vector<OpenMM::Vec3>& forces) const {
+    for (auto iter = order.rbegin(); iter != order.rend(); ++iter) {
+        int i = *iter;
+        Vec3 f = forces[i];
+        if (dynamic_cast<const TwoParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A two particle average.
+
+            const TwoParticleAverageSite& site = dynamic_cast<const TwoParticleAverageSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1);
+            double w1 = site.getWeight(0), w2 = site.getWeight(1);
+            forces[p1] += f*w1;
+            forces[p2] += f*w2;
+        }
+        else if (dynamic_cast<const ThreeParticleAverageSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A three particle average.
+
+            const ThreeParticleAverageSite& site = dynamic_cast<const ThreeParticleAverageSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
+            double w1 = site.getWeight(0), w2 = site.getWeight(1), w3 = site.getWeight(2);
+            forces[p1] += f*w1;
+            forces[p2] += f*w2;
+            forces[p3] += f*w3;
+        }
+        else if (dynamic_cast<const OutOfPlaneSite*>(&system.getVirtualSite(i)) != NULL) {
+            // An out of plane site.
+
+            const OutOfPlaneSite& site = dynamic_cast<const OutOfPlaneSite&>(system.getVirtualSite(i));
+            int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
+            double w12 = site.getWeight12(), w13 = site.getWeight13(), wcross = site.getWeightCross();
+            Vec3 v12 = atomCoordinates[p2]-atomCoordinates[p1];
+            Vec3 v13 = atomCoordinates[p3]-atomCoordinates[p1];
+            Vec3 f2(w12*f[0] - wcross*v13[2]*f[1] + wcross*v13[1]*f[2],
+                    wcross*v13[2]*f[0] + w12*f[1] - wcross*v13[0]*f[2],
+                   -wcross*v13[1]*f[0] + wcross*v13[0]*f[1] + w12*f[2]);
+            Vec3 f3(w13*f[0] + wcross*v12[2]*f[1] - wcross*v12[1]*f[2],
+                   -wcross*v12[2]*f[0] + w13*f[1] + wcross*v12[0]*f[2],
+                    wcross*v12[1]*f[0] - wcross*v12[0]*f[1] + w13*f[2]);
+            forces[p1] += f-f2-f3;
+            forces[p2] += f2;
+            forces[p3] += f3;
+        }
+        else if (dynamic_cast<const LocalCoordinatesSite*>(&system.getVirtualSite(i)) != NULL) {
+            // A local coordinates site.
+
+            const LocalCoordinatesSite& site = dynamic_cast<const LocalCoordinatesSite&>(system.getVirtualSite(i));
+            int numParticles = site.getNumParticles();
+            vector<double> originWeights, wx, wy;
+            site.getOriginWeights(originWeights);
+            site.getXWeights(wx);
+            site.getYWeights(wy);
+            Vec3 xdir, ydir;
+            for (int j = 0; j < numParticles; j++) {
+                Vec3 pos = atomCoordinates[site.getParticle(j)];
+                xdir += pos*wx[j];
+                ydir += pos*wy[j];
             }
-            else if (dynamic_cast<const OutOfPlaneSite*>(&system.getVirtualSite(i)) != NULL) {
-                // An out of plane site.
-                
-                const OutOfPlaneSite& site = dynamic_cast<const OutOfPlaneSite&>(system.getVirtualSite(i));
-                int p1 = site.getParticle(0), p2 = site.getParticle(1), p3 = site.getParticle(2);
-                double w12 = site.getWeight12(), w13 = site.getWeight13(), wcross = site.getWeightCross();
-                Vec3 v12 = atomCoordinates[p2]-atomCoordinates[p1];
-                Vec3 v13 = atomCoordinates[p3]-atomCoordinates[p1];
-                Vec3 f2(w12*f[0] - wcross*v13[2]*f[1] + wcross*v13[1]*f[2],
-                        wcross*v13[2]*f[0] + w12*f[1] - wcross*v13[0]*f[2],
-                       -wcross*v13[1]*f[0] + wcross*v13[0]*f[1] + w12*f[2]);
-                Vec3 f3(w13*f[0] + wcross*v12[2]*f[1] - wcross*v12[1]*f[2],
-                       -wcross*v12[2]*f[0] + w13*f[1] + wcross*v12[0]*f[2],
-                        wcross*v12[1]*f[0] - wcross*v12[0]*f[1] + w13*f[2]);
-                forces[p1] += f-f2-f3;
-                forces[p2] += f2;
-                forces[p3] += f3;
+            Vec3 localPosition = site.getLocalPosition();
+            Vec3 zdir = xdir.cross(ydir);
+            double normXdir = sqrt(xdir.dot(xdir));
+            double normZdir = sqrt(zdir.dot(zdir));
+            double invNormXdir = (normXdir > 0.0 ? 1.0/normXdir : 0.0);
+            double invNormZdir = (normZdir > 0.0 ? 1.0/normZdir : 0.0);
+            Vec3 dx = xdir*invNormXdir;
+            Vec3 dz = zdir*invNormZdir;
+            Vec3 dy = dz.cross(dx);
+
+            // The derivatives for this case are very complicated.  They were computed with SymPy then simplified by hand.
+
+            vector<double> wxScaled(numParticles);
+            for (int j = 0; j < numParticles; j++)
+                wxScaled[j] = wx[j]*invNormXdir;
+            Vec3 fp1 = localPosition*f[0];
+            Vec3 fp2 = localPosition*f[1];
+            Vec3 fp3 = localPosition*f[2];
+            for (int j = 0; j < numParticles; j++) {
+                double t1 = (wx[j]*ydir[0]-wy[j]*xdir[0])*invNormZdir;
+                double t2 = (wx[j]*ydir[1]-wy[j]*xdir[1])*invNormZdir;
+                double t3 = (wx[j]*ydir[2]-wy[j]*xdir[2])*invNormZdir;
+                double sx = t3*dz[1]-t2*dz[2];
+                double sy = t1*dz[2]-t3*dz[0];
+                double sz = t2*dz[0]-t1*dz[1];
+                int p = site.getParticle(j);
+                forces[p][0] += fp1[0]*wxScaled[j]*(1-dx[0]*dx[0]) + fp1[2]*(dz[0]*sx   ) + fp1[1]*((-dx[0]*dy[0]      )*wxScaled[j] + dy[0]*sx - dx[1]*t2 - dx[2]*t3) + f[0]*originWeights[j];
+                forces[p][1] += fp1[0]*wxScaled[j]*( -dx[0]*dx[1]) + fp1[2]*(dz[0]*sy+t3) + fp1[1]*((-dx[1]*dy[0]-dz[2])*wxScaled[j] + dy[0]*sy + dx[1]*t1);
+                forces[p][2] += fp1[0]*wxScaled[j]*( -dx[0]*dx[2]) + fp1[2]*(dz[0]*sz-t2) + fp1[1]*((-dx[2]*dy[0]+dz[1])*wxScaled[j] + dy[0]*sz + dx[2]*t1);
+                forces[p][0] += fp2[0]*wxScaled[j]*( -dx[1]*dx[0]) + fp2[2]*(dz[1]*sx-t3) - fp2[1]*(( dx[0]*dy[1]-dz[2])*wxScaled[j] - dy[1]*sx - dx[0]*t2);
+                forces[p][1] += fp2[0]*wxScaled[j]*(1-dx[1]*dx[1]) + fp2[2]*(dz[1]*sy   ) - fp2[1]*(( dx[1]*dy[1]      )*wxScaled[j] - dy[1]*sy + dx[0]*t1 + dx[2]*t3) + f[1]*originWeights[j];
+                forces[p][2] += fp2[0]*wxScaled[j]*( -dx[1]*dx[2]) + fp2[2]*(dz[1]*sz+t1) - fp2[1]*(( dx[2]*dy[1]+dz[0])*wxScaled[j] - dy[1]*sz - dx[2]*t2);
+                forces[p][0] += fp3[0]*wxScaled[j]*( -dx[2]*dx[0]) + fp3[2]*(dz[2]*sx+t2) + fp3[1]*((-dx[0]*dy[2]-dz[1])*wxScaled[j] + dy[2]*sx + dx[0]*t3);
+                forces[p][1] += fp3[0]*wxScaled[j]*( -dx[2]*dx[1]) + fp3[2]*(dz[2]*sy-t1) + fp3[1]*((-dx[1]*dy[2]+dz[0])*wxScaled[j] + dy[2]*sy + dx[1]*t3);
+                forces[p][2] += fp3[0]*wxScaled[j]*(1-dx[2]*dx[2]) + fp3[2]*(dz[2]*sz   ) + fp3[1]*((-dx[2]*dy[2]      )*wxScaled[j] + dy[2]*sz - dx[0]*t1 - dx[1]*t2) + f[2]*originWeights[j];
             }
-            else if (dynamic_cast<const LocalCoordinatesSite*>(&system.getVirtualSite(i)) != NULL) {
-                // A local coordinates site.
-                
-                const LocalCoordinatesSite& site = dynamic_cast<const LocalCoordinatesSite&>(system.getVirtualSite(i));
-                int numParticles = site.getNumParticles();
-                vector<double> originWeights, wx, wy;
-                site.getOriginWeights(originWeights);
-                site.getXWeights(wx);
-                site.getYWeights(wy);
-                Vec3 xdir, ydir;
-                for (int j = 0; j < numParticles; j++) {
-                    Vec3 pos = atomCoordinates[site.getParticle(j)];
-                    xdir += pos*wx[j];
-                    ydir += pos*wy[j];
-                }
-                Vec3 localPosition = site.getLocalPosition();
-                Vec3 zdir = xdir.cross(ydir);
-                double normXdir = sqrt(xdir.dot(xdir));
-                double normZdir = sqrt(zdir.dot(zdir));
-                double invNormXdir = (normXdir > 0.0 ? 1.0/normXdir : 0.0);
-                double invNormZdir = (normZdir > 0.0 ? 1.0/normZdir : 0.0);
-                Vec3 dx = xdir*invNormXdir;
-                Vec3 dz = zdir*invNormZdir;
-                Vec3 dy = dz.cross(dx);
-                
-                // The derivatives for this case are very complicated.  They were computed with SymPy then simplified by hand.
-                
-                vector<double> wxScaled(numParticles);
-                for (int j = 0; j < numParticles; j++)
-                    wxScaled[j] = wx[j]*invNormXdir;
-                Vec3 fp1 = localPosition*f[0];
-                Vec3 fp2 = localPosition*f[1];
-                Vec3 fp3 = localPosition*f[2];
-                for (int j = 0; j < numParticles; j++) {
-                    double t1 = (wx[j]*ydir[0]-wy[j]*xdir[0])*invNormZdir;
-                    double t2 = (wx[j]*ydir[1]-wy[j]*xdir[1])*invNormZdir;
-                    double t3 = (wx[j]*ydir[2]-wy[j]*xdir[2])*invNormZdir;
-                    double sx = t3*dz[1]-t2*dz[2];
-                    double sy = t1*dz[2]-t3*dz[0];
-                    double sz = t2*dz[0]-t1*dz[1];
-                    int p = site.getParticle(j);
-                    forces[p][0] += fp1[0]*wxScaled[j]*(1-dx[0]*dx[0]) + fp1[2]*(dz[0]*sx   ) + fp1[1]*((-dx[0]*dy[0]      )*wxScaled[j] + dy[0]*sx - dx[1]*t2 - dx[2]*t3) + f[0]*originWeights[j];
-                    forces[p][1] += fp1[0]*wxScaled[j]*( -dx[0]*dx[1]) + fp1[2]*(dz[0]*sy+t3) + fp1[1]*((-dx[1]*dy[0]-dz[2])*wxScaled[j] + dy[0]*sy + dx[1]*t1);
-                    forces[p][2] += fp1[0]*wxScaled[j]*( -dx[0]*dx[2]) + fp1[2]*(dz[0]*sz-t2) + fp1[1]*((-dx[2]*dy[0]+dz[1])*wxScaled[j] + dy[0]*sz + dx[2]*t1);
-                    forces[p][0] += fp2[0]*wxScaled[j]*( -dx[1]*dx[0]) + fp2[2]*(dz[1]*sx-t3) - fp2[1]*(( dx[0]*dy[1]-dz[2])*wxScaled[j] - dy[1]*sx - dx[0]*t2);
-                    forces[p][1] += fp2[0]*wxScaled[j]*(1-dx[1]*dx[1]) + fp2[2]*(dz[1]*sy   ) - fp2[1]*(( dx[1]*dy[1]      )*wxScaled[j] - dy[1]*sy + dx[0]*t1 + dx[2]*t3) + f[1]*originWeights[j];
-                    forces[p][2] += fp2[0]*wxScaled[j]*( -dx[1]*dx[2]) + fp2[2]*(dz[1]*sz+t1) - fp2[1]*(( dx[2]*dy[1]+dz[0])*wxScaled[j] - dy[1]*sz - dx[2]*t2);
-                    forces[p][0] += fp3[0]*wxScaled[j]*( -dx[2]*dx[0]) + fp3[2]*(dz[2]*sx+t2) + fp3[1]*((-dx[0]*dy[2]-dz[1])*wxScaled[j] + dy[2]*sx + dx[0]*t3);
-                    forces[p][1] += fp3[0]*wxScaled[j]*( -dx[2]*dx[1]) + fp3[2]*(dz[2]*sy-t1) + fp3[1]*((-dx[1]*dy[2]+dz[0])*wxScaled[j] + dy[2]*sy + dx[1]*t3);
-                    forces[p][2] += fp3[0]*wxScaled[j]*(1-dx[2]*dx[2]) + fp3[2]*(dz[2]*sz   ) + fp3[1]*((-dx[2]*dy[2]      )*wxScaled[j] + dy[2]*sz - dx[0]*t1 - dx[1]*t2) + f[2]*originWeights[j];
-                }
-           }
-        }
+       }
+    }
 }

plugins/drude/platforms/reference/src/ReferenceDrudeKernels.cpp

@@ -61,6 +61,11 @@ static ReferenceConstraints& extractConstraints(ContextImpl& context) {
     return *data->constraints;
 }
 
+static const ReferenceVirtualSites& extractVirtualSites(ContextImpl& context) {
+    ReferencePlatform::PlatformData* data = reinterpret_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    return *data->virtualSites;
+}
+
 static double computeShiftedKineticEnergy(ContextImpl& context, vector<double>& inverseMasses, double timeShift) {
     const System& system = context.getSystem();
     int numParticles = system.getNumParticles();
@@ -374,7 +379,7 @@ void ReferenceIntegrateDrudeLangevinStepKernel::execute(ContextImpl& context, co
             }
         }
     }
-    ReferenceVirtualSites::computePositions(context.getSystem(), pos);
+    extractVirtualSites(context).computePositions(context.getSystem(), pos);
     data.time += integrator.getStepSize();
     data.stepCount++;
 }
@@ -452,7 +457,7 @@ void ReferenceIntegrateDrudeSCFStepKernel::execute(ContextImpl& context, const D
     
     // Update the positions of virtual sites and Drude particles.
     
-    ReferenceVirtualSites::computePositions(context.getSystem(), pos);
+    extractVirtualSites(context).computePositions(context.getSystem(), pos);
     minimize(context, integrator.getMinimizationErrorTolerance());
     data.time += integrator.getStepSize();
     data.stepCount++;

tests/TestVirtualSites.h

@@ -482,6 +482,36 @@ void testOverlappingSites() {
         ASSERT_EQUAL_VEC(s1.getForces()[i], s2.getForces()[i], 1e-5);
 }
 
+/**
+ * Test virtual sites that depend on other virtual sites.
+ */
+void testNestedSites() {
+    System system;
+    system.addParticle(1.0);
+    for (int i = 0; i < 3; i++)
+        system.addParticle(0.0);
+    system.addParticle(1.0);
+    system.setVirtualSite(2, new TwoParticleAverageSite(0, 4, 0.5, 0.5));
+    system.setVirtualSite(1, new TwoParticleAverageSite(0, 2, 0.5, 0.5));
+    system.setVirtualSite(3, new TwoParticleAverageSite(2, 4, 0.5, 0.5));
+    CustomExternalForce* force = new CustomExternalForce("-c*x");
+    force->addPerParticleParameter("c");
+    force->addParticle(1, {1.0});
+    force->addParticle(3, {2.0});
+    system.addForce(force);
+    vector<Vec3> positions(5);
+    positions[4] = Vec3(0, 0, 4.0);
+    VerletIntegrator integrator(0.002);
+    Context context(system, integrator, platform);
+    context.setPositions(positions);
+    context.computeVirtualSites();
+    State state = context.getState(State::Positions | State::Forces);
+    for (int i = 0; i < 5; i++)
+        ASSERT_EQUAL_VEC(Vec3(0, 0, i), state.getPositions()[i], 1e-6);
+    ASSERT_EQUAL_VEC(Vec3(1*0.75 + 2*0.25, 0, 0), state.getForces()[0], 1e-6);
+    ASSERT_EQUAL_VEC(Vec3(1*0.25 + 2*0.75, 0, 0), state.getForces()[4], 1e-6);
+}
+
 void runPlatformTests();
 
 int main(int argc, char* argv[]) {
@@ -496,6 +526,7 @@ int main(int argc, char* argv[]) {
         testLocalCoordinates(4);
         testConservationLaws();
         testOverlappingSites();
+        testNestedSites();
         runPlatformTests();
     }
     catch(const exception& e) {