void
check_3j_family_j_gsl (const int two_j1, const int two_j2,
const int two_m1, const int two_m2)
{
double *a;
int two_jmin, two_jmax, imax, i;
int two_m3 = -(two_m1 + two_m2);
wigner3j_family_j (two_j1, two_j2, two_m1, two_m2, &a, &two_jmin, &two_jmax);
imax = (two_jmax-two_jmin)/2;
printf ("two_j1: %d two_j2: %d two_m1: %d two_m2: %d\n",
two_j1, two_j2, two_m1, two_m2);
for(i=0; i<=imax; i++)
{
int two_j3=two_jmin+i*2;
double gsl=gsl_sf_coupling_3j(two_j1, two_j2, two_j3,
two_m1, two_m2, two_m3);
printf ("\ttwo_j3: %d\t\twigner: %g\tgsl: %g\tdiff: %g\n",
two_j3, a[i], gsl, a[i]-gsl);
}
free (a);
}
void
hammer_3j_j (const int two_jmax)
{
double *a;
int two_j2, two_j3, two_m2, two_m3, tjmax, tjmin;
for (two_j2 = 0; two_j2 <= two_jmax; two_j2++)
for (two_m2 = -two_j2; two_m2 <=two_j2; two_m2 += 2)
for (two_j3 = 0; two_j3 <= two_jmax; two_j3++)
for (two_m3 = -two_j3; two_m3 <=two_j3; two_m3+=2)
{
printf ("%d %d %d %d\n", two_j2, two_j3, two_m2, two_m3);
wigner3j_family_j (two_j2, two_j3, two_m2, two_m3, &a, &tjmax, &tjmin);
free (a);
}
}
double
wigner3j (const int two_j1, const int two_j2, const int two_j3,
const int two_m1, const int two_m2, const int two_m3)
/* Returns a single Wigner 3J symbol. Computation is done by
calculating the family of 3J symbols by J recursion with two_j2 and
two_j3 fixed, and returning the symbol corresponding to the
specified value of two_j1. In most cases this will require less
computation than using M recursion. */
{
int a = abs (two_j2 - two_j3);
int b = abs (two_m2 + two_m3);
int two_jmin = __MAX(a, b);
int two_jmax = two_j2 + two_j3;
int dim = 1 + (two_jmax - two_jmin) / 2;
double buff[__MAX (dim, 1)]; /* Don't want 0 or negative size here. */
/* Check that |m| <= j */
if ((abs (two_m1) > two_j1) ||
(abs (two_m2) > two_j2) ||
(abs (two_m3) > two_j3))
return NAN;
/* Check (j,m) pairs are both integer or both half integer */
if (__ODD (two_m2 + two_j2) ||
__ODD (two_m2 + two_j2) ||
__ODD (two_m3 + two_j3))
return NAN;
/* Check for positive j */
if (two_j1 < 0 || two_j2 < 0 || two_j3 < 0)
return NAN;
/* Check sum of Ms is 0 */
if (two_m1 + two_m2 + two_m3 != 0)
return 0.0;
/* And, finally check triangle condition is met */
if (!is_triangle (two_j1, two_j2, two_j3))
return 0.0;
wigner3j_family_j (two_j2, two_j3, two_m2, two_m3,
buff, &two_jmin, &two_jmax);
return buff[(two_j1 - two_jmin) / 2];
}
void
check_3j_family_j (const int two_j1, const int two_j2,
const int two_m1, const int two_m2)
{
double *a;
int two_jmin, two_jmax, imax, i;
wigner3j_family_j (two_j1, two_j2, two_m1, two_m2, &a, &two_jmin, &two_jmax);
imax = (two_jmax-two_jmin)/2;
printf ("two_j1: %d two_j2: %d two_m1: %d two_m2: %d\n",
two_j1, two_j2, two_m1, two_m2);
for(i=0; i<=imax; i++)
{
int j=two_jmin+i;
printf ("\ttwo_j3: %d\t %g\n", j, a[i]);
}
free (a);
}
void
check_3j_family_j_exact_2 (const int two_jmax)
{
int two_j;
printf("two_j\trecursive\tgsl\texact\trec-ex\tgsl-ex\n");
for (two_j = 0; two_j <=two_jmax; two_j = (two_j + 1)*100)
{
double exact = 1.0 / sqrt (two_j + 1.0);
double gsl = gsl_sf_coupling_3j(two_j, two_j, 0, 0, 0, 0);
double *a;
int tjmax, tjmin;
wigner3j_family_j (two_j, two_j, 0, 0, &a, &tjmax, &tjmin);
printf("%d\t%g\t%g\t%g\t%g\t%g\n", two_j, a[0],gsl, exact, a[0]-exact, gsl-exact);
free (a);
}
}
void
check_3j_family_j_exact_1 (const int two_jmax)
{
int two_j;
for (two_j = 0; two_j <=two_jmax; two_j = (two_j + 1)*100-1)
{
double exact = 1.0 / sqrt (two_j + 1.0);
double gsl = gsl_sf_coupling_3j(two_j, two_j, 0, two_j, -two_j, 0);
double *a;
int tjmax, tjmin;
wigner3j_family_j (two_j, two_j, two_j, -two_j, &a, &tjmax, &tjmin);
printf ("two_j: %d\trecursive: % .18e\t exact: % .18e\tdiff: % .18e\n",
two_j, a[0], exact, a[0]-exact);
printf ("two_j: %d\t gsl: % .18e\t exact: % .18e\tdiff: % .18e\n",
two_j, gsl, exact, gsl-exact);
free (a);
}
}
