/** * Enforce constraints on SETTLE clusters */ __kernel void applySettle(int numClusters, float tol, __global const float4* restrict oldPos, __global float4* restrict posDelta, __global const float4* restrict velm, __global const int4* restrict clusterAtoms, __global const float2* restrict clusterParams) { int index = get_global_id(0); while (index < numClusters) { // Load the data for this cluster. int4 atoms = clusterAtoms[index]; float2 params = clusterParams[index]; float4 apos0 = oldPos[atoms.x]; float4 xp0 = posDelta[atoms.x]; float4 apos1 = oldPos[atoms.y]; float4 xp1 = posDelta[atoms.y]; float4 apos2 = oldPos[atoms.z]; float4 xp2 = posDelta[atoms.z]; float m0 = RECIP(velm[atoms.x].w); float m1 = RECIP(velm[atoms.y].w); float m2 = RECIP(velm[atoms.z].w); // Apply the SETTLE algorithm. float xb0 = apos1.x-apos0.x; float yb0 = apos1.y-apos0.y; float zb0 = apos1.z-apos0.z; float xc0 = apos2.x-apos0.x; float yc0 = apos2.y-apos0.y; float zc0 = apos2.z-apos0.z; float invTotalMass = 1.0f/(m0+m1+m2); float xcom = (xp0.x*m0 + (xb0+xp1.x)*m1 + (xc0+xp2.x)*m2) * invTotalMass; float ycom = (xp0.y*m0 + (yb0+xp1.y)*m1 + (yc0+xp2.y)*m2) * invTotalMass; float zcom = (xp0.z*m0 + (zb0+xp1.z)*m1 + (zc0+xp2.z)*m2) * invTotalMass; float xa1 = xp0.x - xcom; float ya1 = xp0.y - ycom; float za1 = xp0.z - zcom; float xb1 = xb0 + xp1.x - xcom; float yb1 = yb0 + xp1.y - ycom; float zb1 = zb0 + xp1.z - zcom; float xc1 = xc0 + xp2.x - xcom; float yc1 = yc0 + xp2.y - ycom; float zc1 = zc0 + xp2.z - zcom; float xaksZd = yb0*zc0 - zb0*yc0; float yaksZd = zb0*xc0 - xb0*zc0; float zaksZd = xb0*yc0 - yb0*xc0; float xaksXd = ya1*zaksZd - za1*yaksZd; float yaksXd = za1*xaksZd - xa1*zaksZd; float zaksXd = xa1*yaksZd - ya1*xaksZd; float xaksYd = yaksZd*zaksXd - zaksZd*yaksXd; float yaksYd = zaksZd*xaksXd - xaksZd*zaksXd; float zaksYd = xaksZd*yaksXd - yaksZd*xaksXd; float axlng = sqrt(xaksXd*xaksXd + yaksXd*yaksXd + zaksXd*zaksXd); float aylng = sqrt(xaksYd*xaksYd + yaksYd*yaksYd + zaksYd*zaksYd); float azlng = sqrt(xaksZd*xaksZd + yaksZd*yaksZd + zaksZd*zaksZd); float trns11 = xaksXd / axlng; float trns21 = yaksXd / axlng; float trns31 = zaksXd / axlng; float trns12 = xaksYd / aylng; float trns22 = yaksYd / aylng; float trns32 = zaksYd / aylng; float trns13 = xaksZd / azlng; float trns23 = yaksZd / azlng; float trns33 = zaksZd / azlng; float xb0d = trns11*xb0 + trns21*yb0 + trns31*zb0; float yb0d = trns12*xb0 + trns22*yb0 + trns32*zb0; float xc0d = trns11*xc0 + trns21*yc0 + trns31*zc0; float yc0d = trns12*xc0 + trns22*yc0 + trns32*zc0; float za1d = trns13*xa1 + trns23*ya1 + trns33*za1; float xb1d = trns11*xb1 + trns21*yb1 + trns31*zb1; float yb1d = trns12*xb1 + trns22*yb1 + trns32*zb1; float zb1d = trns13*xb1 + trns23*yb1 + trns33*zb1; float xc1d = trns11*xc1 + trns21*yc1 + trns31*zc1; float yc1d = trns12*xc1 + trns22*yc1 + trns32*zc1; float zc1d = trns13*xc1 + trns23*yc1 + trns33*zc1; // --- Step2 A2' --- float rc = 0.5*params.y; float rb = sqrt(params.x*params.x-rc*rc); float ra = rb*(m1+m2)*invTotalMass; rb -= ra; float sinphi = za1d / ra; float cosphi = sqrt(1.0f - sinphi*sinphi); float sinpsi = (zb1d - zc1d) / (2*rc*cosphi); float cospsi = sqrt(1.0f - sinpsi*sinpsi); float ya2d = ra*cosphi; float xb2d = - rc*cospsi; float yb2d = - rb*cosphi - rc*sinpsi*sinphi; float yc2d = - rb*cosphi + rc*sinpsi*sinphi; float xb2d2 = xb2d*xb2d; float hh2 = 4.0f*xb2d2 + (yb2d-yc2d)*(yb2d-yc2d) + (zb1d-zc1d)*(zb1d-zc1d); float deltx = 2.0f*xb2d + sqrt(4.0f*xb2d2 - hh2 + params.y*params.y); xb2d -= deltx*0.5; // --- Step3 al,be,ga --- float alpha = (xb2d*(xb0d-xc0d) + yb0d*yb2d + yc0d*yc2d); float beta = (xb2d*(yc0d-yb0d) + xb0d*yb2d + xc0d*yc2d); float gamma = xb0d*yb1d - xb1d*yb0d + xc0d*yc1d - xc1d*yc0d; float al2be2 = alpha*alpha + beta*beta; float sintheta = (alpha*gamma - beta*sqrt(al2be2 - gamma*gamma)) / al2be2; // --- Step4 A3' --- float costheta = sqrt(1.0f - sintheta*sintheta); float xa3d = - ya2d*sintheta; float ya3d = ya2d*costheta; float za3d = za1d; float xb3d = xb2d*costheta - yb2d*sintheta; float yb3d = xb2d*sintheta + yb2d*costheta; float zb3d = zb1d; float xc3d = - xb2d*costheta - yc2d*sintheta; float yc3d = - xb2d*sintheta + yc2d*costheta; float zc3d = zc1d; // --- Step5 A3 --- float xa3 = trns11*xa3d + trns12*ya3d + trns13*za3d; float ya3 = trns21*xa3d + trns22*ya3d + trns23*za3d; float za3 = trns31*xa3d + trns32*ya3d + trns33*za3d; float xb3 = trns11*xb3d + trns12*yb3d + trns13*zb3d; float yb3 = trns21*xb3d + trns22*yb3d + trns23*zb3d; float zb3 = trns31*xb3d + trns32*yb3d + trns33*zb3d; float xc3 = trns11*xc3d + trns12*yc3d + trns13*zc3d; float yc3 = trns21*xc3d + trns22*yc3d + trns23*zc3d; float zc3 = trns31*xc3d + trns32*yc3d + trns33*zc3d; xp0.x = xcom + xa3; xp0.y = ycom + ya3; xp0.z = zcom + za3; xp1.x = xcom + xb3 - xb0; xp1.y = ycom + yb3 - yb0; xp1.z = zcom + zb3 - zb0; xp2.x = xcom + xc3 - xc0; xp2.y = ycom + yc3 - yc0; xp2.z = zcom + zc3 - zc0; // Record the new positions. posDelta[atoms.x] = xp0; posDelta[atoms.y] = xp1; posDelta[atoms.z] = xp2; index += get_global_size(0); } } /** * Enforce velocity constraints on SETTLE clusters */ __kernel void constrainVelocities(int numClusters, float tol, __global const float4* restrict oldPos, __global float4* restrict posDelta, __global float4* restrict velm, __global const int4* restrict clusterAtoms, __global const float2* restrict clusterParams) { for (int index = get_global_id(0); index < numClusters; index += get_global_size(0)) { // Load the data for this cluster. int4 atoms = clusterAtoms[index]; float4 apos0 = oldPos[atoms.x]; float4 apos1 = oldPos[atoms.y]; float4 apos2 = oldPos[atoms.z]; float4 v0 = velm[atoms.x]; float4 v1 = velm[atoms.y]; float4 v2 = velm[atoms.z]; // Compute intermediate quantities: the atom masses, the bond directions, the relative velocities, // and the angle cosines and sines. float mA = RECIP(v0.w); float mB = RECIP(v1.w); float mC = RECIP(v2.w); float4 eAB = apos1-apos0; float4 eBC = apos2-apos1; float4 eCA = apos0-apos2; eAB.xyz /= SQRT(eAB.x*eAB.x + eAB.y*eAB.y + eAB.z*eAB.z); eBC.xyz /= SQRT(eBC.x*eBC.x + eBC.y*eBC.y + eBC.z*eBC.z); eCA.xyz /= SQRT(eCA.x*eCA.x + eCA.y*eCA.y + eCA.z*eCA.z); float vAB = (v1.x-v0.x)*eAB.x + (v1.y-v0.y)*eAB.y + (v1.z-v0.z)*eAB.z; float vBC = (v2.x-v1.x)*eBC.x + (v2.y-v1.y)*eBC.y + (v2.z-v1.z)*eBC.z; float vCA = (v0.x-v2.x)*eCA.x + (v0.y-v2.y)*eCA.y + (v0.z-v2.z)*eCA.z; float cA = -(eAB.x*eCA.x + eAB.y*eCA.y + eAB.z*eCA.z); float cB = -(eAB.x*eBC.x + eAB.y*eBC.y + eAB.z*eBC.z); float cC = -(eBC.x*eCA.x + eBC.y*eCA.y + eBC.z*eCA.z); float s2A = 1-cA*cA; float s2B = 1-cB*cB; float s2C = 1-cC*cC; // Solve the equations. These are different from those in the SETTLE paper (JCC 13(8), pp. 952-962, 1992), because // in going from equations B1 to B2, they make the assumption that mB=mC (but don't bother to mention they're // making that assumption). We allow all three atoms to have different masses. float mABCinv = RECIP(mA*mB*mC); float denom = (((s2A*mB+s2B*mA)*mC+(s2A*mB*mB+2*(cA*cB*cC+1)*mA*mB+s2B*mA*mA))*mC+s2C*mA*mB*(mA+mB))*mABCinv; float tab = ((cB*cC*mA-cA*mB-cA*mC)*vCA + (cA*cC*mB-cB*mC-cB*mA)*vBC + (s2C*mA*mA*mB*mB*mABCinv+(mA+mB+mC))*vAB)/denom; float tbc = ((cA*cB*mC-cC*mB-cC*mA)*vCA + (s2A*mB*mB*mC*mC*mABCinv+(mA+mB+mC))*vBC + (cA*cC*mB-cB*mA-cB*mC)*vAB)/denom; float tca = ((s2B*mA*mA*mC*mC*mABCinv+(mA+mB+mC))*vCA + (cA*cB*mC-cC*mB-cC*mA)*vBC + (cB*cC*mA-cA*mB-cA*mC)*vAB)/denom; v0.xyz += (tab*eAB.xyz - tca*eCA.xyz)*v0.w; v1.xyz += (tbc*eBC.xyz - tab*eAB.xyz)*v1.w; v2.xyz += (tca*eCA.xyz - tbc*eBC.xyz)*v2.w; velm[atoms.x] = v0; velm[atoms.y] = v1; velm[atoms.z] = v2; } }