double doublefact(int n){
if(n==-1) return 1;
else if (n==0) return 1;
else if (n==1) return 1;
else return n*doublefact(n-2);
}
double volintegral (double d1, double d2, double d3, int l, int m, int n, int shape)
{
if ((l%2==1) || (m%2==1) || (n%2==1)) return 0.0;
else
switch (shape) {
/* ell. cylinder shape */
case 1: return 4.0*PI*pow(d1, l+1)*pow(d2, m+1)*pow(d3, n+1)/(double)(n+1)
*doublefact(l-1)*doublefact(m-1)/doublefact(l+m+2);
/* spheroid shape */
case 2: return 4.0*PI*pow(d1, l+1)*pow(d2, m+1)*pow(d3, n+1)
*doublefact(l-1)*doublefact(m-1)*doublefact(n-1)/
doublefact(l+m+n+3);
/* rp shape */
default: return 8.0/((l+1)*(m+1)*(n+1))*pow(d1, l+1)*pow(d2,m+1)*
pow(d3, n+1);
}
}
std::vector<contr_t> slater_fit_midpoint(double zeta, int am, int nf) {
// Returned basis
std::vector<contr_t> ret(nf);
// Weight must have decayed to
const double decayfac=1e-6;
// Determine the limits
double min, max;
determine_slater_limits(zeta,am,decayfac,min,max);
// Convert to logarithm scale used in the integration
min=log10(min);
max=log10(max);
// printf("lower=%e, max at %e, upper=%e\n",min,log10(maxz),max);
// Quadrature points
std::vector<double> lga(nf);
double dlga=(max-min)/nf;
// Form quadrature points
for(int i=0;i<nf;i++) {
lga[i]=min+(i+0.5)*dlga;
ret[i].z=pow(10.0,lga[i]);
}
// Initialize weights
for(int i=0;i<nf;i++) {
ret[i].c=0.0;
}
// Common factor is
double cfac=pow(zeta,am+5.0/2.0)/(pow(2.0,5.0/4.0)*pow(M_PI,1.0/4.0))*sqrt(doublefact(2*am+1)/fact(2*am+2))/log(10.0)*dlga;
// Calculate weights using midpoint method
for(int i=0;i<nf;i++)
ret[i].c=cfac*calc_slater_weight(zeta,ret[i].z,am);
return ret;
}