/*
$Id: tt.c 19707 2010-10-29 17:59:36Z d3y133 $
*/
Vall_match = Vall[match];
dVall_match = (1.0/(al*r[match]))*Derivative7_4(match,Vall);
ddVall_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,Vall)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,Vall);
rc[0] = 1.0;
rc[1] = r[match];
for (i=2; i<13; ++i)
rc[i] = rc[1]*rc[i-1];
/* debug */
for (i=0; i<Ngrid; ++i)
upp[i] = (2.0*Vall[i] + l*(l+1.0)/(r[i]*r[i]) - 2.0*el)*ul[i];
upp_match = upp[match];
uppp_match = (1.0/(al*r[match]))*Derivative7_4(match,upp);
upppp_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,upp)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,upp);
printf("dVall_match = %le\n", dVall_match);
printf("ddVall_match = %le\n", ddVall_match);
/******************************************/
/* Calculate the all-electron core charge */
/******************************************/
ae_core_charge = Norm_LogGrid(match,(l+1.0),ul);
printf("ae_core_charge = %le\n",ae_core_charge);
void init_xpansion(int l_in,
int match_in,
double occupation_in,
double el_in,
double *Vall_in,
double *ul_in,
double *ul_prime_in,
double *Vl_in,
double *wl_in,
double *wl_prime_in)
{
int i,iteration;
double gamma,gamma_mid,dgamma;
double constraint1,constraint2,constraint_mid;
double gamma1,gamma2;
double Vall_match, dVall_match,ddVall_match;
double al;
double *r;
r = r_LogGrid();
al = log_amesh_LogGrid();
l = l_in;
match = match_in;
occupation = occupation_in;
el = el_in;
Vall = Vall_in;
ul = ul_in;
ul_prime = ul_prime_in;
Vl = Vl_in;
wl = wl_in;
wl_prime = wl_prime_in;
/* fix ul_prime = (d/dr)ul, rather then (d/di)ul */
ldpsi = ul_prime[match]/(al*r[match]*ul[match]);
Vall_match = Vall[match];
dVall_match = (1.0/(al*r[match]))*Derivative7_4(match,Vall);
ddVall_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,Vall)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,Vall);
rc[0] = 1.0;
rc[1] = r[match];
for (i=2; i<13; ++i)
rc[i] = rc[1]*rc[i-1];
/******************************************/
/* Calculate the all-electron core charge */
/******************************************/
ae_core_charge = Norm_LogGrid(match,(l+1.0),ul);
/**************************************************************/
/* define p(rcl), p'(rcl), p''(rcl), p'''(rcl) and p''''(rcl) */
/**************************************************************/
poly[0] = log(ul[match]/pow(rc[1],(l+1.0)));
poly[1] = ldpsi - (l+1.0)/rc[1];
poly[2] = 2.0*Vall_match
- 2.0*el
- (2.0*(l+1.0)/rc[1])*poly[1]
- poly[1]*poly[1];
poly[3] = 2.0*dVall_match
+ (2.0*(l+1.0)/rc[2])*poly[1]
- (2.0*(l+1.0)/rc[1])*poly[2]
- 2.0*poly[1]*poly[2];
poly[4] = 2.0*ddVall_match
- (4.0*(l+1.0)/rc[3])*poly[1]
+ (4.0*(l+1.0)/rc[2])*poly[2]
- (2.0*(l+1.0)/rc[1])*poly[3]
- 2.0*poly[2]*poly[2]
- 2.0*poly[1]*poly[3];
/* get initial guess for gamma */
get_c0_c10();
/* Bracket gamma, so that constraint==0 can be found */
gamma1 = c[1];
gamma2 = -c[1];
constraint1 = get_c0_c12(gamma1);
constraint2 = get_c0_c12(gamma2);
iteration = 0;
while ((constraint1*constraint2 > 0.0) && (iteration <=50))
{
++iteration;
if (fabs(constraint1) < fabs(constraint2))
{
gamma1 = gamma1 + 1.6*(gamma1-gamma2);
constraint1 = get_c0_c12(gamma1);
}
else
{
gamma2 = gamma2 + 1.6*(gamma2-gamma1);
constraint2 = get_c0_c12(gamma2);
}
}
/* perform bisection of gamma1 and gamma2 until constraint==0 */
constraint1 = get_c0_c12(gamma1);
constraint2 = get_c0_c12(gamma2);
if (constraint1 < 0.0)
{
gamma = gamma1;
dgamma = (gamma2-gamma1);
}
else
{
gamma = gamma2;
dgamma = (gamma1-gamma2);
}
iteration = 0;
constraint_mid = 1.0;
while ((fabs(dgamma) > SMALL) && (constraint_mid != 0.0) && (iteration<=80))
{
++iteration;
dgamma = 0.5*dgamma;
gamma_mid = gamma+dgamma;
constraint_mid = get_c0_c12(gamma_mid);
if (constraint_mid < 0.0)
gamma = gamma_mid;
}
} /*init_xpansion */
int init_xpansion2(int l_in,
int match_in,
double el_in,
double *Vall_in,
double *ul_in,
double *ul_prime_in,
double *Vl_in,
double *wl_in,
double *wl_prime_in)
{
int i;
double Vall_match, dVall_match,ddVall_match;
double al;
double *r;
r = r_LogGrid();
al = log_amesh_LogGrid();
l = l_in;
match = match_in;
el = el_in;
Vall = Vall_in;
ul = ul_in;
ul_prime = ul_prime_in;
Vl = Vl_in;
wl = wl_in;
wl_prime = wl_prime_in;
/* fix ul_prime = (d/dr)ul, rather then (d/di)ul */
ldpsi = ul_prime[match]/(al*r[match]*ul[match]);
Vall_match = Vall[match];
dVall_match = (1.0/(al*r[match]))*Derivative7_4(match,Vall);
ddVall_match = (-1.0/(r[match]*r[match]*al)) *Derivative7_4(match,Vall)
+ (+1.0/(r[match]*r[match]*al*al))*Laplacian7_4(match,Vall);
rc[0] = 1.0;
rc[1] = r[match];
for (i=2; i<13; ++i)
rc[i] = rc[1]*rc[i-1];
/**************************************************************/
/* define p(rcl), p'(rcl), p''(rcl), p'''(rcl) and p''''(rcl) */
/**************************************************************/
poly[0] = log(ul[match]/pow(rc[1],(l+1.0)));
poly[1] = ldpsi - (l+1.0)/rc[1];
poly[2] = 2.0*Vall_match
- 2.0*el
- (2.0*(l+1.0)/rc[1])*poly[1]
- poly[1]*poly[1];
poly[3] = 2.0*dVall_match
+ (2.0*(l+1.0)/rc[2])*poly[1]
- (2.0*(l+1.0)/rc[1])*poly[2]
- 2.0*poly[1]*poly[2];
poly[4] = 2.0*ddVall_match
- (4.0*(l+1.0)/rc[3])*poly[1]
+ (4.0*(l+1.0)/rc[2])*poly[2]
- (2.0*(l+1.0)/rc[1])*poly[3]
- 2.0*poly[2]*poly[2]
- 2.0*poly[1]*poly[3];
/* generate trouulier-Martin expansion, if possible */
return get_c0_c10_xpansion2();
} /*init_xpansion2 */