EwaldPeriodic(const matrix3<>& R, int nAtoms) : R(R), G((2*M_PI)*inv(R)), RTR((~R)*R), GGT(G*(~G)) { logPrintf("\n---------- Setting up ewald sum ----------\n"); //Determine optimum gaussian width for Ewald sums: // From below, the number of reciprocal cells ~ Prod_k |R.column[k]| // and number of real space cells ~ Prod_k |G.row[k]| // including the fact that the real space cost ~ Natoms^2/cell // and the reciprocal space cost ~ Natoms/cell sigma = 1.; for(int k=0; k<3; k++) sigma *= R.column(k).length() / G.row(k).length(); sigma = pow(sigma/std::max(1,nAtoms), 1./6); logPrintf("Optimum gaussian width for ewald sums = %lf bohr.\n", sigma); //Carry real space sums to Rmax = 10 sigma and Gmax = 10/sigma //This leads to relative errors ~ 1e-22 in both sums, well within double precision limits for(int k=0; k<3; k++) { Nreal[k] = 1+ceil(CoulombKernel::nSigmasPerWidth * G.row(k).length() * sigma / (2*M_PI)); Nrecip[k] = 1+ceil(CoulombKernel::nSigmasPerWidth * R.column(k).length() / (2*M_PI*sigma)); } logPrintf("Real space sum over %d unit cells with max indices ", (2*Nreal[0]+1)*(2*Nreal[1]+1)*(2*Nreal[2]+1)); Nreal.print(globalLog, " %d "); logPrintf("Reciprocal space sum over %d terms with max indices ", (2*Nrecip[0]+1)*(2*Nrecip[1]+1)*(2*Nrecip[2]+1)); Nrecip.print(globalLog, " %d "); }
void Basis::setup(const GridInfo& gInfo, const IonInfo& iInfo, double Ecut, const vector3<> k) { //Find the indices within Ecut: vector3<int> iGbox; for(int i=0; i<3; i++) iGbox[i] = 1 + int(sqrt(2*Ecut) * gInfo.R.column(i).length() / (2*M_PI)); std::vector< vector3<int> > iGvec; std::vector<int> indexVec; vector3<int> iG; for(iG[0]=-iGbox[0]; iG[0]<=iGbox[0]; iG[0]++) for(iG[1]=-iGbox[1]; iG[1]<=iGbox[1]; iG[1]++) for(iG[2]=-iGbox[2]; iG[2]<=iGbox[2]; iG[2]++) if(0.5*dot(iG+k, gInfo.GGT*(iG+k)) <= Ecut) { iGvec.push_back(iG); indexVec.push_back(gInfo.fullGindex(iG)); } setup(gInfo, iInfo, indexVec, iGvec); logPrintf("nbasis = %lu for k = ", nbasis); k.print(globalLog, " %6.3f "); }