/****************************************
Function name : solve_pseudo_orbitals
Description :
Return type : void
Author : Marat Valiev
Date & Time : 4/7/99 2:31:16 PM
****************************************/
void paw_generate_pseudo_orbitals()
{
int i;
int k;
int Ngrid;
int max_iter;
int converged;
int iteration;
int match;
int status;
double log_amesh;
double f1,f2;
double *V;
double *rgrid;
double *f;
double norm;
char output[300];
FILE *fp;
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
log_amesh = paw_log_amesh_LogGrid();
/*set maximum number of iterations*/
max_iter = 600;
for (i = 0; i <= nbasis-1; i++)
{
iteration = 0;
converged = False;
status = False;
match = i_r_orbital[i];
/*Start the selfconsistent loop over given ps state */
while ((iteration <= max_iter) && (!converged))
{
++iteration;
/* get pseudopotential*/
V = paw_get_paw_potential(i);
/*
if(orb_type[i]==bound || orb_type[i]==virt)
{
status = paw_R_Schrodinger(prin_n_ps[i],
orb_l[i],
V,
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
}
else if(orb_type[i]==scattering)
{
status = paw_R_Schrodinger_Fixed_Logderiv(prin_n_ps[i],
orb_l[i],
V,
match,
log_deriv[i],
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
}
else
{
printf("unknown orbital type\n");
exit(1);
}
*/
status = paw_R_Schrodinger_Fixed_Logderiv(prin_n_ps[i],
orb_l[i],
V,
match,
log_deriv[i],
&e_ps[i],
phi_ps[i],
phi_ps_prime[i]);
/*Update pseudopotential potential*/
paw_update_paw_potential(&converged, i, e[i], e_ps[i],phi_ps[i]);
}
/*report on convergence status*/
if (converged && (status))
{
if (paw_debug()) printf("\n%d%d pseudo orbital with the eigenvalue=%f has been found\n",
prin_n[i], orb_l[i], e_ps[i]);
}
else
{
if (paw_debug()) printf("Unable to find %d%d orbital\n ",
prin_n[i], orb_l[i]);
}
norm = phi[i][match]/phi_ps[i][match];
/*scale ps orbital */
for (k=0;k<=match;k++)
{
phi_ps[i][k]=phi_ps[i][k]*norm;
phi_ps_prime[i][k]=phi_ps_prime[i][k]*norm;
}
for (k=match+1;k<=Ngrid-1;k++)
{
phi_ps[i][k]=phi[i][k];
phi_ps_prime[i][k]=phi_prime[i][k];
}
}
if (paw_debug())
{
for (i = 0; i <= nbasis-1; ++i)
{
sprintf(output, "%s%s%d%d", paw_sdir(),"test",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; k++)
{
fprintf(fp, "%f\t%f\t%f\n", rgrid[k], phi[i][k],phi_ps[i][k]);
}
fclose(fp);
}
}
pseudo_orbitals_done = True;
/* save original basis functions */
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
phi0[i][k] = phi[i][k];
phi0_prime[i][k] = phi_prime[i][k];
phi_ps0[i][k] = phi_ps[i][k];
phi_ps0_prime[i][k] = phi_ps_prime[i][k];
}
}
/* calculate densities */
paw_Zero_LogGrid(rho);
paw_Zero_LogGrid(rho_ps);
for (i = 0; i <= nbasis-1; i++)
{
for (k = 0; k <= Ngrid-1; k++)
{
rho[k] += fill[i]*pow((phi0[i][k]/rgrid[k]),2.0);
rho_ps[k] += fill[i]*pow((phi_ps0[i][k]/rgrid[k]),2.0);
}
}
/*calculate kinetic energy*/
ekin = paw_get_kinetic_energy(nbasis, orb_l, fill, phi, phi_prime);
f = paw_alloc_LogGrid();
for (i = 0; i <= nbasis-1; i++)
{
for (k=0; k<=Ngrid-1; k++)
{
f[k] = 0.5*phi_prime[i][k]/(rgrid[k]*log_amesh)*
phi_prime[i][k]/(rgrid[k]*log_amesh) -
0.5*phi_ps_prime[i][k]/(rgrid[k]*log_amesh)*
phi_ps_prime[i][k]/(rgrid[k]*log_amesh);
}
f1 = paw_Def_Integr(0.0,f,0.0,Ngrid-1);
for (k=0; k<=Ngrid-1; k++)
{
f[k] = 0.5*phi_prime[i][k]/(rgrid[k]*log_amesh)*
phi_prime[i][k]/(rgrid[k]*log_amesh);
}
f2 = paw_Def_Integr(0.0,f,0.0,Ngrid-1);
delta_ekin[i] = (int)(100*f1/f2);
if (paw_debug())
printf("kinetic energy of the %d%s orbital was reduced by %d%s\n",
prin_n[i],paw_spd_Name(orb_l[i]),delta_ekin[i],"%");
}
paw_dealloc_LogGrid(f);
}
void paw_generate_projectors_vanderbilt()
{
int i;
int j;
int k;
int Ngrid;
double norm;
double max_prj;
double max_phi;
double max_phi_ps;
double tmp_prj;
double *V_ref;
double *V;
double *rgrid;
double **b;
double **prj_ps0;
char output[300];
FILE *fp;
/*make sure the pseudo orbitalas were found*/
if (! pseudo_orbitals_done)
{
printf("cannot calculate projectors\n");
printf("pseudo basis is not ready\n");
exit(1);
}
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
b = paw_alloc_2d_array(nbasis,nbasis);
prj_ps0 = paw_alloc_2d_array(nbasis,Ngrid);
/*obtain the ref potential*/
V_ref = paw_get_ref_pot();
/*form initial guess for projectors as in Blochl*/
for (i = 0; i < nbasis; ++i)
{
V = paw_get_paw_potential(i);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = (V_ref[k] - V[k])*phi_ps[i][k];
if (paw_debug())
{
sprintf(output, "%s%s_%d%d", paw_sdir(),"p",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; ++k)
{
fprintf(fp, "%le\t %le\t %le \n", rgrid[k], prj_ps[i][k],(V_ref[k] - V[k]));
}
fclose(fp);
}
}
/*check for accidental null projectors*/
for (i = 0; i < nbasis; ++i)
{
max_prj = 0.0;
for (k = 0; k < Ngrid; ++k)
{
tmp_prj = fabs(prj_ps[i][k]);
if (tmp_prj > max_prj)
max_prj = tmp_prj;
}
if (max_prj <0.000001)
{
printf("found null projectors, aborting the program ... \n");
exit(1);
}
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
if (orb_l[i] == orb_l[j] )
{
b[i][j] = paw_dot_product(phi_ps[j],prj_ps[i]);
}
else
{
b[i][j] = 0.0;
}
}
}
paw_get_inverse(b,nbasis);
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps0[i][k] = prj_ps[i][k];
}
for (i=0;i<=nbasis-1;i++)
{
paw_Zero_LogGrid(prj_ps[i]);
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps[i][k] = prj_ps[i][k] + b[i][j]*prj_ps0[j][k];
}
}
for (i=0;i<=nbasis-1;i++)
{
norm = paw_dot_product(prj_ps[i],phi_ps[i]);
if (fabs(norm) < SMALL)
{
printf("division by zero while normalizing prj_pss");
exit(99);
}
if (paw_debug()) printf("prj_ps norm=%le\n",norm);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = prj_ps[i][k]/norm;
}
/*rescale basis*/
for (i = 0; i <= nbasis-1; i++)
{
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < i_r_orbital[i]; k++)
{
if (max_prj < fabs(prj_ps[i][k]))
max_prj = fabs(prj_ps[i][k]);
if (max_phi_ps < fabs(phi_ps[i][k]))
max_phi_ps = fabs(phi_ps[i][k]);
}
if (max_prj == 0.0 || max_phi_ps == 0.0)
{
printf("division by zero while rescaling basis\n");
exit(99);
}
norm = 0.75*sqrt(max_phi_ps/max_prj);
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < Ngrid; ++k)
{
prj_ps[i][k] = prj_ps[i][k]*norm;
phi[i][k] = phi[i][k]/norm;
phi_ps[i][k] = phi_ps[i][k]/norm;
phi_prime[i][k] = phi_prime[i][k]/norm;
phi_ps_prime[i][k] = phi_ps_prime[i][k]/norm;
}
}
}
void paw_generate_projectors_blochl()
{
int i;
int j;
int k;
int Ngrid;
double norm;
double max_prj;
double max_phi;
double max_phi_ps;
double tmp_prj;
double *V_ref;
double *V;
double *rgrid;
double **b;
double **L;
double **U;
double **L_inv;
double **U_inv;
double **test_matrix;
char output[300];
FILE *fp;
/*make sure the pseudo orbitalas were found*/
if (! pseudo_orbitals_done)
{
printf("cannot calculate projectors\n");
printf("pseudo basis is not ready\n");
exit(1);
}
Ngrid = paw_N_LogGrid();
rgrid = paw_r_LogGrid();
b = paw_alloc_2d_array(nbasis,nbasis);
L = paw_alloc_2d_array(nbasis,nbasis);
L_inv = paw_alloc_2d_array(nbasis,nbasis);
U = paw_alloc_2d_array(nbasis,nbasis);
U_inv = paw_alloc_2d_array(nbasis,nbasis);
test_matrix = paw_alloc_2d_array(nbasis,nbasis);
/*obtain the ref potential*/
V_ref = paw_get_ref_pot();
/*form initial guess for projectors as in Blochl*/
for (i = 0; i < nbasis; ++i)
{
V = paw_get_paw_potential(i);
for (k = 0; k < Ngrid; ++k)
prj_ps[i][k] = (V_ref[k] - V[k])*phi_ps[i][k];
if (paw_debug())
{
sprintf(output, "%s%s_%d%d", paw_sdir(),"p",prin_n[i],orb_l[i]);
fp = fopen(output, "w+");
for (k = 0; k < Ngrid; ++k)
{
fprintf(fp, "%le\t %le\t %le \n", rgrid[k], prj_ps[i][k],(V_ref[k] - V[k]));
}
fclose(fp);
}
}
/*check for accidental null projectors*/
for (i = 0; i < nbasis; ++i)
{
max_prj = 0.0;
for (k = 0; k < Ngrid; ++k)
{
tmp_prj = fabs(prj_ps[i][k]);
if (tmp_prj > max_prj)
max_prj = tmp_prj;
}
if (max_prj <0.000001)
{
printf("found null projectors, aborting the program ... \n");
exit(1);
}
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
if (orb_l[i] == orb_l[j] )
{
b[i][j] = paw_dot_product(phi_ps[j],prj_ps[i]);
}
else
{
b[i][j] = 0.0;
}
}
}
paw_lu_decompose(nbasis, b, L, U);
paw_triang_matrix_inverse("l",nbasis,L,L_inv);
paw_triang_matrix_inverse("u",nbasis,U,U_inv);
for (i=0;i<=nbasis-1;i++)
{
for (k = 0; k <= Ngrid-1; k++)
prj_ps0[i][k] = prj_ps[i][k];
}
for (i=0;i<=nbasis-1;i++)
{
paw_Zero_LogGrid(prj_ps[i]);
paw_Zero_LogGrid(phi[i]);
paw_Zero_LogGrid(phi_ps[i]);
paw_Zero_LogGrid(phi_prime[i]);
paw_Zero_LogGrid(phi_ps_prime[i]);
}
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=i;j++)
{
for (k = 0; k <= Ngrid-1; k++)
{
prj_ps[i][k] = prj_ps[i][k] + L_inv[i][j]*prj_ps0[j][k];
phi[i][k] = phi[i][k] + U_inv[j][i]*phi0[j][k];
phi_ps[i][k] = phi_ps[i][k] + U_inv[j][i]*phi_ps0[j][k];
phi_prime[i][k] = phi_prime[i][k] + U_inv[j][i]*phi0_prime[j][k];
phi_ps_prime[i][k] = phi_ps_prime[i][k] + U_inv[j][i]*phi_ps0_prime[j][k];
}
}
}
for (i=0;i<=nbasis-1;i++)
paw_Zero_LogGrid(prj_ps0[i]);
for (i=0;i<=nbasis-1;i++)
{
for (j=0;j<=nbasis-1;j++)
{
for (k = 0; k <= Ngrid-1; k++)
{
prj_ps0[i][k] = prj_ps0[i][k] + U_inv[i][j]*prj_ps[j][k];
}
}
}
/*rescale basis*/
for (i = 0; i <= nbasis-1; i++)
{
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
for (k = 0; k < i_r_orbital[i]; k++)
{
if (max_prj < fabs(prj_ps[i][k]))
max_prj = fabs(prj_ps[i][k]);
if (max_phi_ps < fabs(phi_ps[i][k]))
max_phi_ps = fabs(phi_ps[i][k]);
}
if (max_prj == 0.0 || max_phi_ps == 0.0)
{
printf("division by zero while rescaling basis\n");
exit(99);
}
norm = 0.75*sqrt(max_phi_ps/max_prj);
max_prj = 0.0;
max_phi = 0.0;
max_phi_ps = 0.0;
scaling_factor[i] = norm;
for (k = 0; k < Ngrid; ++k)
{
prj_ps[i][k] = prj_ps[i][k]*norm;
phi[i][k] = phi[i][k]/norm;
phi_ps[i][k] = phi_ps[i][k]/norm;
phi_prime[i][k] = phi_prime[i][k]/norm;
phi_ps_prime[i][k] = phi_ps_prime[i][k]/norm;
}
}
for (i = 0; i <= nbasis-1; i++)
{
for (j = 0; j <= nbasis-1; j++)
{
tr_matrix[i][j] = U_inv[i][j];
}
}
if (paw_debug())
printf("derivative=%f\n",phi_ps_prime[0][0]/(rgrid[0]*paw_log_amesh_LogGrid()));
}
