void Potential::generate_local_potential()
{
PROFILE_WITH_TIMER("sirius::Potential::generate_local_potential");
mdarray<double, 2> vloc_radial_integrals(unit_cell_.num_atom_types(), ctx_.gvec().num_shells());
/* split G-shells between MPI ranks */
splindex<block> spl_gshells(ctx_.gvec().num_shells(), comm_.size(), comm_.rank());
#pragma omp parallel
{
/* splines for all atom types */
std::vector< Spline<double> > sa(unit_cell_.num_atom_types());
for (int iat = 0; iat < unit_cell_.num_atom_types(); iat++)
sa[iat] = Spline<double>(unit_cell_.atom_type(iat).radial_grid());
#pragma omp for
for (int igsloc = 0; igsloc < spl_gshells.local_size(); igsloc++)
{
int igs = spl_gshells[igsloc];
for (int iat = 0; iat < unit_cell_.num_atom_types(); iat++)
{
auto& atom_type = unit_cell_.atom_type(iat);
if (igs == 0)
{
for (int ir = 0; ir < atom_type.num_mt_points(); ir++)
{
double x = atom_type.radial_grid(ir);
sa[iat][ir] = (x * atom_type.uspp().vloc[ir] + atom_type.zn()) * x;
}
vloc_radial_integrals(iat, igs) = sa[iat].interpolate().integrate(0);
}
else
{
double g = ctx_.gvec().shell_len(igs);
double g2 = std::pow(g, 2);
for (int ir = 0; ir < atom_type.num_mt_points(); ir++)
{
double x = atom_type.radial_grid(ir);
sa[iat][ir] = (x * atom_type.uspp().vloc[ir] + atom_type.zn() * gsl_sf_erf(x)) * std::sin(g * x);
}
vloc_radial_integrals(iat, igs) = (sa[iat].interpolate().integrate(0) / g - atom_type.zn() * std::exp(-g2 / 4) / g2);
}
}
}
}
int ld = unit_cell_.num_atom_types();
comm_.allgather(vloc_radial_integrals.at<CPU>(), ld * spl_gshells.global_offset(), ld * spl_gshells.local_size());
auto v = unit_cell_.make_periodic_function(vloc_radial_integrals, ctx_.gvec());
ctx_.fft().prepare(ctx_.gvec().partition());
ctx_.fft().transform<1>(ctx_.gvec().partition(), &v[ctx_.gvec().partition().gvec_offset_fft()]);
ctx_.fft().output(&local_potential_->f_rg(0));
ctx_.fft().dismiss();
}
/** type = 0: full-potential radial integrals \n
* type = 1: pseudopotential valence density integrals \n
* type = 2: pseudopotential code density integrals
*/
mdarray<double, 2> Density::generate_rho_radial_integrals(int type__)
{
runtime::Timer t("sirius::Density::generate_rho_radial_integrals");
mdarray<double, 2> rho_radial_integrals(unit_cell_.num_atom_types(), ctx_.gvec().num_shells());
/* split G-shells between MPI ranks */
splindex<block> spl_gshells(ctx_.gvec().num_shells(), ctx_.comm().size(), ctx_.comm().rank());
if (type__ == 4)
{
/* rho[r_] := Z*b^3/8/Pi*Exp[-b*r]
* Integrate[Sin[G*r]*rho[r]*r*r/(G*r), {r, 0, \[Infinity]}, Assumptions -> {G >= 0, b > 0}]
* Out[] = (b^4 Z)/(4 (b^2 + G^2)^2 \[Pi])
*/
double b = 4;
for (int igs = 0; igs < ctx_.gvec().num_shells(); igs++)
{
double G = ctx_.gvec().shell_len(igs);
for (int iat = 0; iat < unit_cell_.num_atom_types(); iat++)
{
rho_radial_integrals(iat, igs) = std::pow(b, 4) * unit_cell_.atom_type(iat).zn() / (4 * std::pow(std::pow(b, 2) + std::pow(G, 2), 2) * pi);
}
}
return rho_radial_integrals;
}
#pragma omp parallel
{
/* splines for all atom types */
std::vector< Spline<double> > sa(unit_cell_.num_atom_types());
for (int iat = 0; iat < unit_cell_.num_atom_types(); iat++)
{
/* full potential radial integrals requre a free atom grid */
sa[iat] = (type__ == 0) ? Spline<double>(unit_cell_.atom_type(iat).free_atom_radial_grid())
: Spline<double>(unit_cell_.atom_type(iat).radial_grid());
}
/* spherical Bessel functions */
Spherical_Bessel_functions jl;
#pragma omp for
for (int igsloc = 0; igsloc < (int)spl_gshells.local_size(); igsloc++)
{
int igs = (int)spl_gshells[igsloc];
for (int iat = 0; iat < unit_cell_.num_atom_types(); iat++)
{
auto& atom_type = unit_cell_.atom_type(iat);
if (type__ == 1 || type__ == 2)
jl = Spherical_Bessel_functions(0, atom_type.radial_grid(), ctx_.gvec().shell_len(igs));
if (type__ == 0)
{
if (igs == 0)
{
for (int ir = 0; ir < sa[iat].num_points(); ir++) sa[iat][ir] = atom_type.free_atom_density(ir);
rho_radial_integrals(iat, igs) = sa[iat].interpolate().integrate(2);
}
else
{
double G = ctx_.gvec().shell_len(igs);
for (int ir = 0; ir < sa[iat].num_points(); ir++)
{
sa[iat][ir] = atom_type.free_atom_density(ir) *
std::sin(G * atom_type.free_atom_radial_grid(ir)) / G;
}
rho_radial_integrals(iat, igs) = sa[iat].interpolate().integrate(1);
}
}
if (type__ == 1)
{
for (int ir = 0; ir < sa[iat].num_points(); ir++)
sa[iat][ir] = jl[0][ir] * atom_type.uspp().total_charge_density[ir];
rho_radial_integrals(iat, igs) = sa[iat].interpolate().integrate(0) / fourpi;
}
if (type__ == 2)
{
for (int ir = 0; ir < sa[iat].num_points(); ir++)
sa[iat][ir] = jl[0][ir] * atom_type.uspp().core_charge_density[ir];
rho_radial_integrals(iat, igs) = sa[iat].interpolate().integrate(2);
}
}
}
}
int ld = unit_cell_.num_atom_types();
ctx_.comm().allgather(rho_radial_integrals.at<CPU>(), static_cast<int>(ld * spl_gshells.global_offset()),
static_cast<int>(ld * spl_gshells.local_size()));
return std::move(rho_radial_integrals);
}