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gint_tools.cpp
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gint_tools.cpp
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//=========================================================
//REFACTOR : Peize Lin, 2021.06.28
//=========================================================
#include "gint_tools.h"
#include <cmath>
#include "module_base/timer.h"
#include "module_base/ylm.h"
#include "module_basis/module_ao/ORB_read.h"
#include "module_hamilt_pw/hamilt_pwdft/global.h"
namespace Gint_Tools
{
int* get_vindex(
const int bxyz,
const int bx,
const int by,
const int bz,
const int nplane,
const int start_ind,
const int ncyz)
{
int *vindex = new int[bxyz];
int bindex = 0;
for(int ii=0; ii<bx; ii++)
{
const int ipart = ii*ncyz;
for(int jj=0; jj<by; jj++)
{
const int jpart = jj*nplane + ipart;
for(int kk=0; kk<bz; kk++)
{
vindex[bindex] = start_ind + kk + jpart;
++bindex;
}
}
}
return vindex;
}
// here vindex refers to local potentials
int* get_vindex(
const int bxyz,
const int bx,
const int by,
const int bz,
const int nplane,
const int ncyz,
const int ibx,
const int jby,
const int kbz)
{
int *vindex = new int[bxyz];
int bindex=0;
// z is the fastest,
// ipart can be obtained by using a previously stored array
for(int ii=0; ii<bx; ii++)
{
const int ipart = (ibx+ii)*ncyz;
for(int jj=0; jj<by; jj++)
{
// jpart can be obtained by using a previously stored array
const int jpart = (jby+jj)*nplane + ipart;
for(int kk=0; kk<bz; kk++)
{
vindex[bindex] = kbz+kk + jpart;
++bindex;
}
}
}
return vindex;
}
// extract the local potentials.
double* get_vldr3(
const double* const vlocal, // vlocal[ir]
const int bxyz,
const int bx,
const int by,
const int bz,
const int nplane,
const int ncyz,
const int ibx,
const int jby,
const int kbz,
const double dv)
{
// set the index for obtaining local potentials
int* vindex = Gint_Tools::get_vindex(bxyz, bx, by, bz, nplane, ncyz, ibx, jby, kbz);
double *vldr3 = new double[bxyz];
for(int ib=0; ib<bxyz; ib++)
{
vldr3[ib]=vlocal[vindex[ib]] * dv;
}
delete[] vindex;
return vldr3;
}
double* get_vldr3(
const double* const vlocal, // vlocal[ir]
const int bxyz,
const int bx,
const int by,
const int bz,
const int nplane,
const int start_ind,
const int ncyz,
const double dv)
{
// set the index for obtaining local potentials
int* vindex = Gint_Tools::get_vindex(bxyz, bx, by, bz, nplane, start_ind, ncyz);
double *vldr3 = new double[bxyz];
for(int ib=0; ib<bxyz; ib++)
{
vldr3[ib]=vlocal[vindex[ib]] * dv;
}
delete[] vindex;
return vldr3;
}
void get_block_info(
const Grid_Technique& gt,
const int bxyz,
const int na_grid,
const int grid_index,
int * &block_iw,
int * &block_index,
int * &block_size,
bool** &cal_flag
)
{
block_iw = new int[na_grid];
block_index = new int[na_grid+1];
block_size = new int[na_grid];
cal_flag = new bool* [bxyz];
for(int ib=0; ib<bxyz; ib++)
{
cal_flag[ib] = new bool[na_grid];
}
block_index[0] = 0;
for (int id=0; id<na_grid; id++)
{
const int mcell_index=gt.bcell_start[grid_index] + id;
const int iat=gt.which_atom[mcell_index]; // index of atom
const int it=GlobalC::ucell.iat2it[ iat ]; // index of atom type
const int ia=GlobalC::ucell.iat2ia[ iat ]; // index of atoms within each type
const int start=GlobalC::ucell.itiaiw2iwt(it, ia, 0); // the index of the first wave function for atom (it,ia)
block_iw[id]=gt.trace_lo[start];
block_index[id+1] = block_index[id]+GlobalC::ucell.atoms[it].nw;
block_size[id]=GlobalC::ucell.atoms[it].nw;
const int imcell=gt.which_bigcell[mcell_index];
const double mt[3] = {
gt.meshball_positions[imcell][0] - gt.tau_in_bigcell[iat][0],
gt.meshball_positions[imcell][1] - gt.tau_in_bigcell[iat][1],
gt.meshball_positions[imcell][2] - gt.tau_in_bigcell[iat][2]};
for(int ib=0; ib<bxyz; ib++)
{
// meshcell_pos: z is the fastest
const double dr[3] = {
gt.meshcell_pos[ib][0] + mt[0],
gt.meshcell_pos[ib][1] + mt[1],
gt.meshcell_pos[ib][2] + mt[2]};
const double distance = std::sqrt(dr[0]*dr[0] + dr[1]*dr[1] + dr[2]*dr[2]); // distance between atom and grid
if(distance > GlobalC::ORB.Phi[it].getRcut() - 1.0e-10)
cal_flag[ib][id]=false;
else
cal_flag[ib][id]=true;
}// end ib
}
}
void cal_psir_ylm(
const Grid_Technique& gt,
const int bxyz,
const int na_grid, // number of atoms on this grid
const int grid_index, // 1d index of FFT index (i,j,k)
const double delta_r, // delta_r of the uniform FFT grid
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const int*const block_size, // block_size[na_grid], number of columns of a band
const bool*const*const cal_flag,
double*const*const psir_ylm) // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
{
ModuleBase::timer::tick("Gint_Tools", "cal_psir_ylm");
std::vector<double> ylma;
for (int id=0; id<na_grid; id++)
{
// there are two parameters we want to know here:
// in which bigcell of the meshball the atom is in?
// what's the cartesian coordinate of the bigcell?
const int mcell_index=gt.bcell_start[grid_index] + id;
const int iat=gt.which_atom[mcell_index]; // index of atom
const int it=GlobalC::ucell.iat2it[iat]; // index of atom type
const Atom*const atom=&GlobalC::ucell.atoms[it];
auto &OrbPhi = GlobalC::ORB.Phi[it];
std::vector<const double*> it_psi_uniform(atom->nw);
std::vector<const double*> it_dpsi_uniform(atom->nw);
// preprocess index
for (int iw=0; iw< atom->nw; ++iw)
{
if ( atom->iw2_new[iw] )
{
auto philn = &OrbPhi.PhiLN(atom->iw2l[iw], atom->iw2n[iw]);
it_psi_uniform[iw] = &philn->psi_uniform[0];
it_dpsi_uniform[iw] = &philn->dpsi_uniform[0];
}
}
// meshball_positions should be the bigcell position in meshball
// to the center of meshball.
// calculated in cartesian coordinates
// the std::vector from the grid which is now being operated to the atom position.
// in meshball language, is the std::vector from imcell to the center cel, plus
// tau_in_bigcell.
const int imcell=gt.which_bigcell[mcell_index];
const double mt[3] = {
gt.meshball_positions[imcell][0] - gt.tau_in_bigcell[iat][0],
gt.meshball_positions[imcell][1] - gt.tau_in_bigcell[iat][1],
gt.meshball_positions[imcell][2] - gt.tau_in_bigcell[iat][2]};
// number of grids in each big cell (bxyz)
for(int ib=0; ib<bxyz; ib++)
{
double *p=&psir_ylm[ib][block_index[id]];
if(!cal_flag[ib][id])
{
ModuleBase::GlobalFunc::ZEROS(p, block_size[id]);
}
else
{
// meshcell_pos: z is the fastest
const double dr[3] = {
gt.meshcell_pos[ib][0] + mt[0],
gt.meshcell_pos[ib][1] + mt[1],
gt.meshcell_pos[ib][2] + mt[2]};
double distance = std::sqrt( dr[0]*dr[0] + dr[1]*dr[1] + dr[2]*dr[2] ); // distance between atom and grid
//if(distance[id] > gt.orbital_rmax) continue;
if (distance < 1.0E-9) distance += 1.0E-9;
//------------------------------------------------------
// spherical harmonic functions Ylm
//------------------------------------------------------
// Ylm::get_ylm_real(this->nnn[it], this->dr[id], ylma);
ModuleBase::Ylm::sph_harm ( GlobalC::ucell.atoms[it].nwl,
dr[0] / distance,
dr[1] / distance,
dr[2] / distance,
ylma);
// these parameters are related to interpolation
// because once the distance from atom to grid point is known,
// we can obtain the parameters for interpolation and
// store them first! these operations can save lots of efforts.
const double position = distance / delta_r;
const int ip = static_cast<int>(position);
const double dx = position - ip;
const double dx2 = dx * dx;
const double dx3 = dx2 * dx;
const double c3 = 3.0*dx2-2.0*dx3;
const double c1 = 1.0-c3;
const double c2 = (dx-2.0*dx2+dx3)*delta_r;
const double c4 = (dx3-dx2)*delta_r;
double phi=0;
for (int iw=0; iw< atom->nw; ++iw)
{
if ( atom->iw2_new[iw] )
{
auto psi_uniform = it_psi_uniform[iw];
auto dpsi_uniform = it_dpsi_uniform[iw];
phi = c1*psi_uniform[ip] + c2*dpsi_uniform[ip] // radial wave functions
+ c3*psi_uniform[ip+1] + c4*dpsi_uniform[ip+1];
}
p[iw]=phi * ylma[atom->iw2_ylm[iw]];
} // end iw
}// end distance<=(GlobalC::ORB.Phi[it].getRcut()-1.0e-15)
}// end ib
}// end id
ModuleBase::timer::tick("Gint_Tools", "cal_psir_ylm");
return;
}
void cal_dpsir_ylm(
const Grid_Technique& gt,
const int bxyz,
const int na_grid, // number of atoms on this grid
const int grid_index, // 1d index of FFT index (i,j,k)
const double delta_r, // delta_r of the uniform FFT grid
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const int*const block_size, // block_size[na_grid], number of columns of a band
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
double*const*const psir_ylm,
double*const*const dpsir_ylm_x,
double*const*const dpsir_ylm_y,
double*const*const dpsir_ylm_z)
{
ModuleBase::timer::tick("Gint_Tools", "cal_dpsir_ylm");
for (int id=0; id<na_grid; id++)
{
const int mcell_index = gt.bcell_start[grid_index] + id;
const int imcell = gt.which_bigcell[mcell_index];
int iat = gt.which_atom[mcell_index];
const int it = GlobalC::ucell.iat2it[iat];
const int ia = GlobalC::ucell.iat2ia[iat];
Atom *atom = &GlobalC::ucell.atoms[it];
const double mt[3]={
gt.meshball_positions[imcell][0] - gt.tau_in_bigcell[iat][0],
gt.meshball_positions[imcell][1] - gt.tau_in_bigcell[iat][1],
gt.meshball_positions[imcell][2] - gt.tau_in_bigcell[iat][2]};
for(int ib=0; ib<bxyz; ib++)
{
double*const p_psi=&psir_ylm[ib][block_index[id]];
double*const p_dpsi_x=&dpsir_ylm_x[ib][block_index[id]];
double*const p_dpsi_y=&dpsir_ylm_y[ib][block_index[id]];
double*const p_dpsi_z=&dpsir_ylm_z[ib][block_index[id]];
if(!cal_flag[ib][id])
{
ModuleBase::GlobalFunc::ZEROS(p_psi, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_x, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_y, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_z, block_size[id]);
}
else
{
const double dr[3]={ // vectors between atom and grid
gt.meshcell_pos[ib][0] + mt[0],
gt.meshcell_pos[ib][1] + mt[1],
gt.meshcell_pos[ib][2] + mt[2]};
double distance = std::sqrt(dr[0]*dr[0] + dr[1]*dr[1] + dr[2]*dr[2]);
//array to store spherical harmonics and its derivatives
std::vector<double> rly;
std::vector<std::vector<double>> grly;
ModuleBase::Ylm::grad_rl_sph_harm(GlobalC::ucell.atoms[it].nwl, dr[0], dr[1], dr[2], rly, grly);
if(distance < 1e-9) distance = 1e-9;
const double position = distance / delta_r;
const double iq = static_cast<int>(position);
const double x0 = position - iq;
const double x1 = 1.0 - x0;
const double x2 = 2.0 - x0;
const double x3 = 3.0 - x0;
const double x12 = x1*x2 / 6;
const double x03 = x0*x3 / 2;
double tmp, dtmp;
for (int iw=0; iw< atom->nw; ++iw)
{
// this is a new 'l', we need 1D orbital wave
// function from interpolation method.
if ( atom->iw2_new[iw] )
{
const Numerical_Orbital_Lm &philn = GlobalC::ORB.Phi[it].PhiLN(
atom->iw2l[iw],
atom->iw2n[iw]);
//if ( iq[id] >= philn.nr_uniform-4)
if ( iq >= philn.nr_uniform-4)
{
tmp = dtmp = 0.0;
}
else
{
// use Polynomia Interpolation method to get the
// wave functions
tmp = x12*(philn.psi_uniform[iq]*x3
+philn.psi_uniform[iq+3]*x0)
+ x03*(philn.psi_uniform[iq+1]*x2
-philn.psi_uniform[iq+2]*x1);
dtmp = x12*(philn.dpsi_uniform[iq]*x3
+philn.dpsi_uniform[iq+3]*x0)
+ x03*(philn.dpsi_uniform[iq+1]*x2
-philn.dpsi_uniform[iq+2]*x1);
}
}//new l is used.
// get the 'l' of this localized wave function
const int ll = atom->iw2l[iw];
const int idx_lm = atom->iw2_ylm[iw];
const double rl = pow(distance, ll);
// 3D wave functions
p_psi[iw] = tmp * rly[idx_lm] / rl;
// derivative of wave functions with respect to atom positions.
const double tmpdphi_rly = (dtmp - tmp * ll / distance) / rl * rly[idx_lm] / distance;
const double tmprl = tmp/rl;
p_dpsi_x[iw] = tmpdphi_rly * dr[0] + tmprl * grly[idx_lm][0];
p_dpsi_y[iw] = tmpdphi_rly * dr[1] + tmprl * grly[idx_lm][1];
p_dpsi_z[iw] = tmpdphi_rly * dr[2] + tmprl * grly[idx_lm][2];
}//iw
}//else
}
}
ModuleBase::timer::tick("Gint_Tools", "cal_dpsir_ylm");
return;
}
void cal_ddpsir_ylm(
const Grid_Technique& gt,
const int bxyz,
const int na_grid, // number of atoms on this grid
const int grid_index, // 1d index of FFT index (i,j,k)
const double delta_r, // delta_r of the uniform FFT grid
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const int*const block_size, // block_size[na_grid], number of columns of a band
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
double*const*const ddpsir_ylm_xx,
double*const*const ddpsir_ylm_xy,
double*const*const ddpsir_ylm_xz,
double*const*const ddpsir_ylm_yy,
double*const*const ddpsir_ylm_yz,
double*const*const ddpsir_ylm_zz)
{
ModuleBase::timer::tick("Gint_Tools", "cal_ddpsir_ylm");
for (int id=0; id<na_grid; id++)
{
const int mcell_index = gt.bcell_start[grid_index] + id;
const int imcell = gt.which_bigcell[mcell_index];
int iat = gt.which_atom[mcell_index];
const int it = GlobalC::ucell.iat2it[iat];
const int ia = GlobalC::ucell.iat2ia[iat];
Atom *atom = &GlobalC::ucell.atoms[it];
const double mt[3]={
gt.meshball_positions[imcell][0] - gt.tau_in_bigcell[iat][0],
gt.meshball_positions[imcell][1] - gt.tau_in_bigcell[iat][1],
gt.meshball_positions[imcell][2] - gt.tau_in_bigcell[iat][2]};
for(int ib=0; ib<bxyz; ib++)
{
double*const p_ddpsi_xx=&ddpsir_ylm_xx[ib][block_index[id]];
double*const p_ddpsi_xy=&ddpsir_ylm_xy[ib][block_index[id]];
double*const p_ddpsi_xz=&ddpsir_ylm_xz[ib][block_index[id]];
double*const p_ddpsi_yy=&ddpsir_ylm_yy[ib][block_index[id]];
double*const p_ddpsi_yz=&ddpsir_ylm_yz[ib][block_index[id]];
double*const p_ddpsi_zz=&ddpsir_ylm_zz[ib][block_index[id]];
if(!cal_flag[ib][id])
{
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_xx, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_xy, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_xz, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_yy, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_yz, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_ddpsi_zz, block_size[id]);
}
else
{
const double dr[3]={ // vectors between atom and grid
gt.meshcell_pos[ib][0] + mt[0],
gt.meshcell_pos[ib][1] + mt[1],
gt.meshcell_pos[ib][2] + mt[2]};
double distance = std::sqrt(dr[0]*dr[0] + dr[1]*dr[1] + dr[2]*dr[2]);
// for some unknown reason, the finite difference between dpsi and ddpsi
// using analytical expression is always wrong; as a result,
// I switch to explicit finite difference method for evaluating
// the second derivatives of the orbitals
if(/*distance < 1e-9*/true)
{
double*** dpsi = new double** [atom->nw];
for(int i=0;i<atom->nw;i++)
{
dpsi[i] = new double*[6];
for(int j=0;j<6;j++)
{
dpsi[i][j] = new double[3];
ModuleBase::GlobalFunc::ZEROS(dpsi[i][j], 3);
}
}
double* dr1 = new double[3];
double** displ = new double* [6];
for(int i=0;i<6;i++)
{
displ[i] = new double[3];
ModuleBase::GlobalFunc::ZEROS(displ[i], 3);
}
displ[0][0] = 0.0001; // in x direction
displ[1][0] = -0.0001;
displ[2][1] = 0.0001; // in y direction
displ[3][1] = -0.0001;
displ[4][2] = 0.0001; // in z direction
displ[5][2] = -0.0001;
for(int i=0;i<6;i++)
{
dr1[0] = dr[0] + displ[i][0];
dr1[1] = dr[1] + displ[i][1];
dr1[2] = dr[2] + displ[i][2];
//array to store spherical harmonics and its derivatives
std::vector<double> rly;
std::vector<std::vector<double>> grly;
ModuleBase::Ylm::grad_rl_sph_harm(GlobalC::ucell.atoms[it].nwl, dr1[0], dr1[1], dr1[2], rly, grly);
double distance1 = std::sqrt(dr1[0]*dr1[0] + dr1[1]*dr1[1] + dr1[2]*dr1[2]);
if(distance1 < 1e-9) distance1 = 1e-9;
const double position = distance1 / delta_r;
const double iq = static_cast<int>(position);
const double x0 = position - iq;
const double x1 = 1.0 - x0;
const double x2 = 2.0 - x0;
const double x3 = 3.0 - x0;
const double x12 = x1*x2 / 6;
const double x03 = x0*x3 / 2;
double tmp, dtmp;
for (int iw=0; iw< atom->nw; ++iw)
{
// this is a new 'l', we need 1D orbital wave
// function from interpolation method.
if ( atom->iw2_new[iw] )
{
const Numerical_Orbital_Lm &philn = GlobalC::ORB.Phi[it].PhiLN(
atom->iw2l[iw],
atom->iw2n[iw]);
//if ( iq[id] >= philn.nr_uniform-4)
if ( iq >= philn.nr_uniform-4)
{
tmp = dtmp = 0.0;
}
else
{
// use Polynomia Interpolation method to get the
// wave functions
tmp = x12*(philn.psi_uniform[iq]*x3
+philn.psi_uniform[iq+3]*x0)
+ x03*(philn.psi_uniform[iq+1]*x2
-philn.psi_uniform[iq+2]*x1);
dtmp = x12*(philn.dpsi_uniform[iq]*x3
+philn.dpsi_uniform[iq+3]*x0)
+ x03*(philn.dpsi_uniform[iq+1]*x2
-philn.dpsi_uniform[iq+2]*x1);
}
}//new l is used.
// get the 'l' of this localized wave function
const int ll = atom->iw2l[iw];
const int idx_lm = atom->iw2_ylm[iw];
const double rl = pow(distance1, ll);
// derivative of wave functions with respect to atom positions.
const double tmpdphi_rly = (dtmp - tmp * ll / distance1) / rl * rly[idx_lm] / distance1;
const double tmprl = tmp/rl;
dpsi[iw][i][0] = tmpdphi_rly * dr1[0] + tmprl * grly[idx_lm][0];
dpsi[iw][i][1] = tmpdphi_rly * dr1[1] + tmprl * grly[idx_lm][1];
dpsi[iw][i][2] = tmpdphi_rly * dr1[2] + tmprl * grly[idx_lm][2];
} // end iw
}//end i = 0-6
for(int iw=0;iw<atom->nw;iw++)
{
p_ddpsi_xx[iw] = (dpsi[iw][0][0] - dpsi[iw][1][0]) / 0.0002;
p_ddpsi_xy[iw] = ((dpsi[iw][2][0] - dpsi[iw][3][0])+(dpsi[iw][0][1] - dpsi[iw][1][1])) / 0.0004;
p_ddpsi_xz[iw] = ((dpsi[iw][4][0] - dpsi[iw][5][0])+(dpsi[iw][0][2] - dpsi[iw][1][2])) / 0.0004;
p_ddpsi_yy[iw] = (dpsi[iw][2][1] - dpsi[iw][3][1]) / 0.0002;
p_ddpsi_yz[iw] = ((dpsi[iw][4][1] - dpsi[iw][5][1])+(dpsi[iw][2][2] - dpsi[iw][3][2])) / 0.0004;
p_ddpsi_zz[iw] = (dpsi[iw][4][2] - dpsi[iw][5][2]) / 0.0002;
}
for(int i=0;i<atom->nw;i++)
{
for(int j=0;j<6;j++)
{
delete[] dpsi[i][j];
}
delete[] dpsi[i];
}
delete[] dpsi;
delete[] dr1;
for(int i=0;i<6;i++)
{
delete[] displ[i];
}
delete[] displ;
}
else
// the analytical method for evaluating 2nd derivatives
// it is not used currently
{
//array to store spherical harmonics and its derivatives
std::vector<double> rly;
std::vector<std::vector<double>> grly;
std::vector<std::vector<double>> hrly;
ModuleBase::Ylm::grad_rl_sph_harm(GlobalC::ucell.atoms[it].nwl, dr[0], dr[1], dr[2], rly, grly);
ModuleBase::Ylm::hes_rl_sph_harm(GlobalC::ucell.atoms[it].nwl, dr[0], dr[1], dr[2], hrly);
const double position = distance / delta_r;
const double iq = static_cast<int>(position);
const double x0 = position - iq;
const double x1 = 1.0 - x0;
const double x2 = 2.0 - x0;
const double x3 = 3.0 - x0;
const double x12 = x1*x2 / 6;
const double x03 = x0*x3 / 2;
double tmp, dtmp, ddtmp;
for (int iw=0; iw< atom->nw; ++iw)
{
// this is a new 'l', we need 1D orbital wave
// function from interpolation method.
if ( atom->iw2_new[iw] )
{
const Numerical_Orbital_Lm &philn = GlobalC::ORB.Phi[it].PhiLN(
atom->iw2l[iw],
atom->iw2n[iw]);
//if ( iq[id] >= philn.nr_uniform-4)
if ( iq >= philn.nr_uniform-4)
{
tmp = dtmp = ddtmp = 0.0;
}
else
{
// use Polynomia Interpolation method to get the
// wave functions
tmp = x12*(philn.psi_uniform[iq]*x3
+philn.psi_uniform[iq+3]*x0)
+ x03*(philn.psi_uniform[iq+1]*x2
-philn.psi_uniform[iq+2]*x1);
dtmp = x12*(philn.dpsi_uniform[iq]*x3
+philn.dpsi_uniform[iq+3]*x0)
+ x03*(philn.dpsi_uniform[iq+1]*x2
-philn.dpsi_uniform[iq+2]*x1);
ddtmp = x12*(philn.ddpsi_uniform[iq]*x3
+philn.ddpsi_uniform[iq+3]*x0)
+ x03*(philn.ddpsi_uniform[iq+1]*x2
-philn.ddpsi_uniform[iq+2]*x1);
}
}//new l is used.
// get the 'l' of this localized wave function
const int ll = atom->iw2l[iw];
const int idx_lm = atom->iw2_ylm[iw];
const double rl = pow(distance, ll);
const double r_lp2 = pow(distance, ll+2);
// d/dr (R_l / r^l)
const double tmpdphi = (dtmp - tmp * ll / distance) / rl;
const double term1 = ddtmp / r_lp2;
const double term2 = (2 * ll + 1) * dtmp / r_lp2 / distance;
const double term3 = ll * (ll + 2) * tmp / r_lp2 / distance / distance;
const double term4 = tmpdphi / distance;
const double term5 = term1 - term2 + term3;
// hessian of (R_l / r^l)
const double term_xx = term4 + dr[0]*dr[0]*term5;
const double term_xy = dr[0]*dr[1]*term5;
const double term_xz = dr[0]*dr[2]*term5;
const double term_yy = term4 + dr[1]*dr[1]*term5;
const double term_yz = dr[1]*dr[2]*term5;
const double term_zz = term4 + dr[2]*dr[2]*term5;
// d/dr (R_l / r^l) * alpha / r
const double term_1x = dr[0] * term4;
const double term_1y = dr[1] * term4;
const double term_1z = dr[2] * term4;
p_ddpsi_xx[iw] = term_xx * rly[idx_lm] + 2.0*term_1x*grly[idx_lm][0] + tmp/rl*hrly[idx_lm][0];
p_ddpsi_xy[iw] = term_xy * rly[idx_lm] + term_1x*grly[idx_lm][1] + term_1y*grly[idx_lm][0] + tmp/rl*hrly[idx_lm][1];
p_ddpsi_xz[iw] = term_xz * rly[idx_lm] + term_1x*grly[idx_lm][2] + term_1z*grly[idx_lm][0] + tmp/rl*hrly[idx_lm][2];
p_ddpsi_yy[iw] = term_yy * rly[idx_lm] + 2.0*term_1y*grly[idx_lm][1] + tmp/rl*hrly[idx_lm][3];
p_ddpsi_yz[iw] = term_yz * rly[idx_lm] + term_1y*grly[idx_lm][2] + term_1z*grly[idx_lm][1] + tmp/rl*hrly[idx_lm][4];
p_ddpsi_zz[iw] = term_zz * rly[idx_lm] + 2.0*term_1z*grly[idx_lm][2] + tmp/rl*hrly[idx_lm][5];
}//iw
} // end if
}//else
}//end ib
}//end id(atom)
ModuleBase::timer::tick("Gint_Tools", "cal_ddpsir_ylm");
return;
}
void cal_dpsirr_ylm(
const Grid_Technique& gt,
const int bxyz,
const int na_grid, // number of atoms on this grid
const int grid_index, // 1d index of FFT index (i,j,k)
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const int*const block_size, // block_size[na_grid], number of columns of a band
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
double*const*const dpsir_ylm_x,
double*const*const dpsir_ylm_y,
double*const*const dpsir_ylm_z,
double*const*const dpsir_ylm_xx,
double*const*const dpsir_ylm_xy,
double*const*const dpsir_ylm_xz,
double*const*const dpsir_ylm_yy,
double*const*const dpsir_ylm_yz,
double*const*const dpsir_ylm_zz)
{
ModuleBase::timer::tick("Gint_Tools", "cal_dpsirr_ylm");
for (int id=0; id<na_grid; id++)
{
const int mcell_index = gt.bcell_start[grid_index] + id;
const int imcell = gt.which_bigcell[mcell_index];
int iat = gt.which_atom[mcell_index];
const int it = GlobalC::ucell.iat2it[iat];
Atom *atom = &GlobalC::ucell.atoms[it];
const double mt[3]={
gt.meshball_positions[imcell][0] - gt.tau_in_bigcell[iat][0],
gt.meshball_positions[imcell][1] - gt.tau_in_bigcell[iat][1],
gt.meshball_positions[imcell][2] - gt.tau_in_bigcell[iat][2]};
for(int ib=0; ib<bxyz; ib++)
{
double*const p_dpsi_x=&dpsir_ylm_x[ib][block_index[id]];
double*const p_dpsi_y=&dpsir_ylm_y[ib][block_index[id]];
double*const p_dpsi_z=&dpsir_ylm_z[ib][block_index[id]];
double*const p_dpsi_xx=&dpsir_ylm_xx[ib][block_index[id]];
double*const p_dpsi_xy=&dpsir_ylm_xy[ib][block_index[id]];
double*const p_dpsi_xz=&dpsir_ylm_xz[ib][block_index[id]];
double*const p_dpsi_yy=&dpsir_ylm_yy[ib][block_index[id]];
double*const p_dpsi_yz=&dpsir_ylm_yz[ib][block_index[id]];
double*const p_dpsi_zz=&dpsir_ylm_zz[ib][block_index[id]];
if(!cal_flag[ib][id])
{
ModuleBase::GlobalFunc::ZEROS(p_dpsi_xx, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_xy, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_xz, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_yy, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_yz, block_size[id]);
ModuleBase::GlobalFunc::ZEROS(p_dpsi_zz, block_size[id]);
}
else
{
const double dr[3]={ // vectors between atom and grid
gt.meshcell_pos[ib][0] + mt[0],
gt.meshcell_pos[ib][1] + mt[1],
gt.meshcell_pos[ib][2] + mt[2]};
for (int iw=0; iw< atom->nw; ++iw)
{
p_dpsi_xx[iw] = p_dpsi_x[iw]*dr[0];
p_dpsi_xy[iw] = p_dpsi_x[iw]*dr[1];
p_dpsi_xz[iw] = p_dpsi_x[iw]*dr[2];
p_dpsi_yy[iw] = p_dpsi_y[iw]*dr[1];
p_dpsi_yz[iw] = p_dpsi_y[iw]*dr[2];
p_dpsi_zz[iw] = p_dpsi_z[iw]*dr[2];
}//iw
}//else
}
}
ModuleBase::timer::tick("Gint_Tools", "cal_dpsirr_ylm");
return;
}
// atomic basis sets
// psir_vlbr3[bxyz][LD_pool]
Gint_Tools::Array_Pool<double> get_psir_vlbr3(
const int bxyz,
const int na_grid, // how many atoms on this (i,j,k) grid
const int LD_pool,
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
const double*const vldr3, // vldr3[bxyz]
const double*const*const psir_ylm) // psir_ylm[bxyz][LD_pool]
{
Gint_Tools::Array_Pool<double> psir_vlbr3(bxyz, LD_pool);
for(int ib=0; ib<bxyz; ++ib)
{
for(int ia=0; ia<na_grid; ++ia)
{
if(cal_flag[ib][ia])
{
for(int i=block_index[ia]; i<block_index[ia+1]; ++i)
{
psir_vlbr3.ptr_2D[ib][i]=psir_ylm[ib][i]*vldr3[ib];
}
}
else
{
for(int i=block_index[ia]; i<block_index[ia+1]; ++i)
{
psir_vlbr3.ptr_2D[ib][i]=0;
}
}
}
}
return psir_vlbr3;
}
void mult_psi_DM(
const Grid_Technique& gt,
const int bxyz,
const int na_grid, // how many atoms on this (i,j,k) grid
const int LD_pool,
const int*const block_iw, // block_iw[na_grid], index of wave functions for each block
const int*const block_size, // block_size[na_grid], number of columns of a band
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
const double*const*const psi, // psir_vlbr3[bxyz][LD_pool]
double ** psi_DM,
const double*const*const DM,
const bool if_symm) // true: density, use dsymv; false: potential/transition density use dgemv
{
constexpr char side='L', uplo='U';
constexpr char transa='N', transb='N';
constexpr double alpha_symm=1, beta=1;
constexpr int inc=1;
double alpha_gemm = if_symm ? 2.0 : 1.0;
for (int ia1=0; ia1<na_grid; ia1++)
{
const int iw1_lo=block_iw[ia1];
if (if_symm)//density
{
//ia1==ia2, diagonal part
// find the first ib and last ib for non-zeros cal_flag
int first_ib=0, last_ib=0;
for(int ib=0; ib<bxyz; ++ib)
{
if(cal_flag[ib][ia1])
{
first_ib=ib;
break;
}
}
for(int ib=bxyz-1; ib>=0; --ib)
{
if(cal_flag[ib][ia1])
{
last_ib=ib+1;
break;
}
}
const int ib_length=last_ib-first_ib;
if(ib_length<=0) continue;
int cal_num=0;
for(int ib=first_ib; ib<last_ib; ++ib)
{
cal_num += cal_flag[ib][ia1];
}
// if enough cal_flag is nonzero
if(cal_num>ib_length/4)
{
dsymm_(&side, &uplo, &block_size[ia1], &ib_length,
&alpha_symm, &DM[iw1_lo][iw1_lo], >.lgd,
&psi[first_ib][block_index[ia1]], &LD_pool,
&beta, &psi_DM[first_ib][block_index[ia1]], &LD_pool);
}
else
{
// int k=1;
for(int ib=first_ib; ib<last_ib; ++ib)
{
if(cal_flag[ib][ia1])
{
dsymv_(&uplo, &block_size[ia1],
&alpha_symm, &DM[iw1_lo][iw1_lo], >.lgd,
&psi[ib][block_index[ia1]], &inc,
&beta, &psi_DM[ib][block_index[ia1]], &inc);
}
}
}
}
int start = if_symm ? ia1 + 1 : 0;
for (int ia2=start; ia2<na_grid; ia2++)
{
int first_ib=0, last_ib=0;
for(int ib=0; ib<bxyz; ++ib)
{
if(cal_flag[ib][ia1] && cal_flag[ib][ia2])
{
first_ib=ib;
break;
}
}
for(int ib=bxyz-1; ib>=0; --ib)
{
if(cal_flag[ib][ia1] && cal_flag[ib][ia2])
{
last_ib=ib+1;
break;
}
}
const int ib_length=last_ib-first_ib;
if(ib_length<=0) continue;
int cal_pair_num=0;
for(int ib=first_ib; ib<last_ib; ++ib)
{
cal_pair_num += cal_flag[ib][ia1] && cal_flag[ib][ia2];
}
const int iw2_lo=block_iw[ia2];
if(cal_pair_num>ib_length/4)
{
dgemm_(&transa, &transb, &block_size[ia2], &ib_length, &block_size[ia1],
&alpha_gemm, &DM[iw1_lo][iw2_lo], >.lgd,
&psi[first_ib][block_index[ia1]], &LD_pool,
&beta, &psi_DM[first_ib][block_index[ia2]], &LD_pool);
}
else
{
for(int ib=first_ib; ib<last_ib; ++ib)
{
if(cal_flag[ib][ia1] && cal_flag[ib][ia2])
{
dgemv_(&transa, &block_size[ia2], &block_size[ia1],
&alpha_gemm, &DM[iw1_lo][iw2_lo], >.lgd,
&psi[ib][block_index[ia1]], &inc,
&beta, &psi_DM[ib][block_index[ia2]], &inc);
}
}
}
}// ia2
} // ia1
}
void mult_psi_DM_new(
const Grid_Technique& gt,
const int bxyz,
const int& grid_index,
const int na_grid, // how many atoms on this (i,j,k) grid
const int LD_pool,
const int*const block_iw, // block_iw[na_grid], index of wave functions for each block
const int*const block_size, // block_size[na_grid], number of columns of a band
const int*const block_index, // block_index[na_grid+1], count total number of atomis orbitals
const bool*const*const cal_flag, // cal_flag[bxyz][na_grid], whether the atom-grid distance is larger than cutoff
const double*const*const psi, // psir_vlbr3[bxyz][LD_pool]
double ** psi_DM,
const hamilt::HContainer<double>* DM,
const bool if_symm) // 1: density, 2: force
{
bool *all_out_of_range = new bool[na_grid];
for(int ia=0; ia<na_grid; ++ia) //number of atoms
{
all_out_of_range[ia] = true;
for(int ib=0; ib<gt.bxyz; ++ib) //number of small box in big box
{
if(cal_flag[ib][ia])
{
all_out_of_range[ia] = false;
//break; //mohan add 2012-07-10
}
}
}
constexpr char side='L', uplo='U';
constexpr char transa='N', transb='N';
constexpr double alpha_symm=1, beta=1;
constexpr int inc=1;
double alpha_gemm = if_symm ? 2.0 : 1.0;
for (int ia1 = 0; ia1 < na_grid; ia1++)
{
if(all_out_of_range[ia1]) continue;
const int mcell_index1 = gt.bcell_start[grid_index] + ia1;
const int iat1 = gt.which_atom[mcell_index1];
const double* tmp_matrix = DM->find_pair(iat1, iat1)->get_pointer(0);
const int iw1_lo=block_iw[ia1];
if (if_symm)//density
{
//ia1==ia2, diagonal part
// find the first ib and last ib for non-zeros cal_flag
int first_ib=0, last_ib=0;
for(int ib=0; ib<bxyz; ++ib)
{
if(cal_flag[ib][ia1])
{