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333 lines (255 loc) · 6.89 KB
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/*
Developed by Roberto Olivares-Amaya and Garnet K.-L. Chan, 2012
Copyright (c) 2012, Garnet K.-L. Chan
This program is integrated in Molpro with the permission of
Sandeep Sharma, Garnet K.-L. Chan and Roberto Olivares-Amaya
*/
#include <stdio.h>
#include <stdlib.h>
#include "new_anglib.h"
#include <cmath>
#include <algorithm>
#include "global.h"
#include <iostream>
using namespace std;
double nine_j(int na, int nb, int nc, int nd, int ne, int nf, int ng, int nh, int ni){
//In this case, we are not dividing by two because that will be done by the
//sixj routine.
//Initializing
double a=na;
double b=nb;
double c=nc;
double d=nd;
double e=ne;
double f=nf;
double g=ng;
double h=nh;
double i=ni;
double ninej=0.0;
//Checking triangle rules
if(na+nb < nc || abs(na-nb) > nc)
return ninej;
if(nd + ne < nf || abs(nd-ne) > nf)
return ninej;
if(ng+nh < ni || abs(ng-nh) > ni)
return ninej;
if(na+nd < ng || abs(na-nd) > ng)
return ninej;
if(nb+ne < nh || abs(nb-ne) > nh)
return ninej;
if(nc+nf < ni || abs(nc-nf) > ni)
return ninej;
double num = 0.0;
double num1 = 0.0;
double num2 = 0.0;
double num3 = 0.0;
double num4 = 0.0;
int kmin = max(max(abs(h-d), abs(b-f)), abs(a-i));
int kmax = min(min( h + d, b + f), a + i);
int k;
//pout << "kmin " << kmin << endl;
//pout << "kmax " << kmax << endl;
for (k = kmin; k <= kmax; k++) {
num1 = k+1;
num2 = six_j(a, b, c, f, i, k);
num3 = six_j(d, e, f, b, k, h);
num4 = six_j(g, h, i, k, a, d);
num=mone(k)*num1*num2*num3*num4;
ninej = ninej + num;
}
return ninej;
}
double six_j(int na, int nb, int nc, int nd, int ne, int nf){
//Initializing
double sixj=0.0;
if((na+nb)%2 != nc%2)
return sixj;
if((nc+nd)%2 != ne%2)
return sixj;
if((na+ne)%2 != nf%2)
return sixj;
if((nb+nd)%2 != nf%2)
return sixj;
if(na + nb < nc || abs(na-nb)>nc)
return sixj;
if(nc+nd<ne || abs(nc-nd)>ne)
return sixj;
if(na+ne<nf || abs(na-ne)>nf)
return sixj;
if(nb+nd<nf || abs(nb-nd)>nf)
return sixj;
//Converting to half its value
double a=na/2.;
double b=nb/2.;
double c=nc/2.;
double d=nd/2.;
double e=ne/2.;
double f=nf/2.;
double num1 = j6_delta(a, b, c);
double num2 = j6_delta(c, d, e);
double num3 = j6_delta(b, d, f);
double den1 = j6_delta(a, e, f);
double pref = num1*num
8000
2*num3/den1;
double square = square_six(a, b, c, d, e, f);
sixj=pref*square;
return sixj;
}
//end six_j
double three_j(int j1, int j2, int j3, int m1, int m2, int m3) {
if(!SpinAdapted::dmrginp.spinAdapted()) {
if(j3 != j1+j2) return 0.0;
else return 1.0;
}
double cleb =0.0;
double threej = 0.0;
double fj1, fj2, fj3, fm3;
fj1 = j1/2.;
fj2 = j2/2.;
fj3 = j3/2.;
fm3 = m3/2.;
cleb = clebsch(j1, m1, j2, m2, j3, m3);
threej = mone(fj1-fj2+fm3)*cleb/sqrt(2*fj3+1);
return threej;
}
double clebsch(int nj1, int nm1, int nj2, int nm2, int nj3, int nm3) {
if(!SpinAdapted::dmrginp.spinAdapted()) {
if(nj3 != nj1+nj2) return 0.0;
else return 1.0;
}
double j1, j2, j3;
double m1, m2, m3;
//Converting to half its value
j1=nj1/2.;
j2=nj2/2.;
j3=nj3/2.;
m1=nm1/2.;
m2=nm2/2.;
m3=nm3/2.;
double cleb=0.0;
if ( j1 < 0 || j2 < 0 || j3 < 0 || abs(m1) > j1 || abs(m2) > j2 ||
abs(m3) > j3 || j1 + j2 < j3 || abs(j1-j2) > j3 || m1 + m2 != m3) {
cleb=0.0;
}
else
{
double factor = 0.0;
double sum = 0.0;
int t;
double num1 = pow(2*j3+1,2);
double num2 = fbinom(j1+j2+j3+1, j1+j2-j3);
double num3 = fbinom(2*j3, j3+m3);
double den1 = (2*j1+1);
double den2 = (2*j2+1);
double den3 = fbinom(j1+j2+j3+1, j1-j2+j3);
double den4 = fbinom(j1+j2+j3+1, j2-j1+j3);
double den5 = fbinom(2*j1, j1+m1);
double den6 = fbinom(2*j2, j2+m2);
double num = num1*num2*num3;
double den = den1*den2*den3*den4*den5*den6;
factor = sqrt(num/den);
double mint = max(max(0., j1-m1-(j3-m3)), j2 + m2 - (j3 + m3));
double maxt = min(min(j1-m1, j2+m2),j1+j2-j3);
//pout << "mint " << mint << endl;
//pout << "maxt " << maxt << endl;
double bin1;
double bin2;
double bin3;
for (t=mint; t<=maxt; t++) {
bin1=fbinom(j1+j2-j3, t);
bin2=fbinom(j3-m3, j1-m1-t);
bin3=fbinom(j3+m3, j2+m2-t);
sum = sum + mone(t)*bin1*bin2*bin3;
//pout << "t " << t << endl;
//pout << "sum " << sum << endl;
//pout << "bin1 " << bin1 << endl;
//pout << "bin2 " << bin2 << endl;
//pout << "bin3 " << bin3 << endl;
}
cleb = factor*sum;
//pout << "factor: " << factor << endl;
//pout << "sum: " << sum << endl;
//pout << "Clebsch: " << cleb << endl;
}
return cleb;
}
double j6_delta(double a, double b, double c) {
double prefac = 0.0;
double den1 = fbinom(a+b+c+1,a+b-c);
//den2 can be substituted to just den=2*c+1, since binom(2*c+1, 2*c) = 2*c+1
//double den2 = fbinom(2*c+1, 2*c);
double den2 = 2*c+1;
double den3 = fbinom(2*c, b+c-a);
double den = den1*den2*den3;
prefac = 1/sqrt(den);
return prefac;
}
double square_six(double a, double b, double c, double d, double e, double f){
/*
[a b c]
[d e f]
*/
int nmin = max(max(max(a+e+f, b+d+f), c+d+e), a+b+c);
int nmax = min(min(a+b+d+e, a+c+d+f), b+c+e+f);
int n;
double num1=0.0;
double num2=0.0;
double num3=0.0;
double num4=0.0;
double num=0.0;
double sum=0.0;
for (n=nmin; n<=nmax; n++){
num1=fbinom(n+1, n-a-e-f);
num2=fbinom(a+e-f, n-b-d-f);
num3=fbinom(a-e+f, n-c-d-e);
num4=fbinom(-a+e+f, n-a-b-c);
num=mone(n)*num1*num2*num3*num4;
sum=sum+num;
}
return sum;
}
double facto(double n) {
double fac;
int nint;
nint = get_cast(n);
fac=1.0;
int i;
if (n==0 || n==1)
return fac;
for (i=2; i<=nint; i++)
fac *= i;
return fac;
}
int mone(double n) {
int value;
int nint;
nint = get_cast(n);
//pout << "nint %2 " << nint %2 << endl;
if (nint % 2 == 0)
value = 1;
else
value = -1;
return (value);
}
int get_cast(double x) {
int i;
//i = (x / (int) x >= 1) ? (int) x : (int) x + 1 ;
i = (int) x;
//pout << "x " << x << " i " << i << endl;
return i;
}
double fbinom(double dn, double dr)
{
double res;
int n = get_cast(dn);
int r = get_cast(dr);
if(n==r || r==0)
{
res = 1.0;
}
else if (r==1)
res = n;
else
res = 1.0*n/(n-r)*fbinom((double)n-1,(double)r);
// pout << n << " " << r<< " -> " << res << endl;
return res;
}