public void SixJProductSum()
{
SixJSymbol[] symbols = GenerateRandomSixJSymbols(50.0, 5);
foreach (SixJSymbol symbol in symbols)
{
Spin a = symbol.J1;
Spin b = symbol.J2;
Spin c = symbol.J4;
Spin d = symbol.J5;
Spin f = symbol.J6;
SpinRange ac = CombinedSpinRange(a, c);
Console.WriteLine("ac: [{0},{1}]", ac.Minimum.J, ac.Maximum.J);
SpinRange bd = CombinedSpinRange(b, d);
Console.WriteLine("bd: [{0},{1}]", bd.Minimum.J, bd.Maximum.J);
SpinRange ac_bd = CombinedSpinRange(ac, bd);
Console.WriteLine("g: [{0},{1}]", ac_bd.Minimum.J, ac_bd.Maximum.J);
Spin[] gs = RandomSpinsInRange(ac_bd, 3);
SpinRange ab = CombinedSpinRange(a, b);
SpinRange cd = CombinedSpinRange(c, d);
SpinRange ab_cd = CombinedSpinRange(ab, cd);
Spin[] xs = AllSpinsInRange(ab_cd);
foreach (Spin g in gs)
{
//double s = 0.0;
List <double> s = new List <double>();
foreach (Spin x in xs)
{
double t = (2.0 * x.J + 1.0) *
SpinMath.SixJ(a, b, x, c, d, f) *
SpinMath.SixJ(c, d, x, b, a, g);
int p = (int)Math.Round(f.J + g.J + x.J);
if (p % 2 != 0)
{
t = -t;
}
Console.WriteLine(" {0} {1}", x.J, t);
//s += t;
s.Add(t);
}
double r = SpinMath.SixJ(a, d, f, b, c, g);
Console.WriteLine("a={0} b={1} c={2} d={3} f={4} g={5}: {6} {7}", a.J, b.J, c.J, d.J, f.J, g.J, s, r);
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(s, r));
//Assert.IsTrue(TestUtilities.IsNearlyEqual(s, r));
}
}
}
private static Spin[] AllSpinsInRange(SpinRange range)
{
int tj_min = (int)Math.Round(2 * range.Minimum.J);
int tj_max = (int)Math.Round(2 * range.Maximum.J);
List <Spin> spins = new List <Spin>();
for (int tj = tj_min; tj <= tj_max; tj += 2)
{
spins.Add(new Spin(tj / 2.0));
}
return(spins.ToArray());
}
private static Spin[] RandomSpinsInRange(SpinRange range, int n)
{
int tj_min = (int)Math.Truncate(2.0 * range.Minimum.J);
int tj_max = (int)Math.Truncate(2.0 * range.Maximum.J);
Spin[] spins = new Spin[n];
Random rng = new Random(1);
for (int i = 0; i < n; i++)
{
spins[i] = new Spin((tj_min + 2 * rng.Next((tj_max - tj_min) / 2 + 1)) / 2.0);
}
return(spins);
}
private static SpinRange CombinedSpinRange(Spin j1, Spin j2)
{
int tj1 = (int)Math.Round(2 * j1.J);
int tj2 = (int)Math.Round(2 * j2.J);
int tj_min = Math.Abs(tj1 - tj2);
int tj_max = tj1 + tj2;
SpinRange range = new SpinRange();
range.Minimum = new Spin(tj_min / 2.0);
range.Maximum = new Spin(tj_max / 2.0);
return(range);
}
public void SixJOrthonormality()
{
SixJSymbol[] sas = GenerateRandomSixJSymbols(50.0, 5);
foreach (SixJSymbol sa in sas)
{
Spin j1 = sa.J1;
Spin j2 = sa.J2;
Spin j4 = sa.J4;
Spin j5 = sa.J5;
Spin j6a = sa.J6;
SpinRange r15 = CombinedSpinRange(j1, j5);
SpinRange r42 = CombinedSpinRange(j4, j2);
SpinRange r6b = CombinedSpinRange(r15, r42);
Spin[] j6bs = RandomSpinsInRange(r6b, 5);
j6bs[0] = j6a;
SpinRange r12 = CombinedSpinRange(j1, j2);
SpinRange r45 = CombinedSpinRange(j4, j5);
SpinRange r3 = CombinedSpinRange(r12, r45);
Spin[] j3s = AllSpinsInRange(r3);
foreach (Spin j6b in j6bs)
{
double s = 0.0;
foreach (Spin j3 in j3s)
{
double t = (2.0 * j3.J + 1.0) *
SpinMath.SixJ(j1, j2, j3, j4, j5, j6a) *
SpinMath.SixJ(j1, j2, j3, j4, j5, j6b);
s += t;
}
Console.WriteLine("j1={0} j2={1} j4={2} j5={3} j6a={4} j6b={5} s={6}", j1.J, j2.J, j4.J, j5.J, j6a.J, j6b.J, s);
if (j6a == j6b)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(s, 1.0 / (2.0 * j6a.J + 1.0)));
}
else
{
Assert.IsTrue(Math.Abs(s) < TestUtilities.TargetPrecision);
}
}
}
}
private static SpinRange CombinedSpinRange(SpinRange r1, SpinRange r2)
{
SpinRange range = new SpinRange();
if (r1.Minimum.J > r2.Minimum.J)
{
range.Minimum = r1.Minimum;
}
else
{
range.Minimum = r2.Minimum;
}
if (r1.Maximum.J < r2.Maximum.J)
{
range.Maximum = r1.Maximum;
}
else
{
range.Maximum = r2.Maximum;
}
return(range);
}
private static SpinRange CombinedSpinRange(SpinRange r1, SpinRange r2)
{
SpinRange range = new SpinRange();
if (r1.Minimum.J > r2.Minimum.J) {
range.Minimum = r1.Minimum;
} else {
range.Minimum = r2.Minimum;
}
if (r1.Maximum.J < r2.Maximum.J) {
range.Maximum = r1.Maximum;
} else {
range.Maximum = r2.Maximum;
}
return (range);
}
private static SpinRange CombinedSpinRange(Spin j1, Spin j2)
{
int tj1 = (int) Math.Round(2 * j1.J);
int tj2 = (int) Math.Round(2 * j2.J);
int tj_min = Math.Abs(tj1 - tj2);
int tj_max = tj1 + tj2;
SpinRange range = new SpinRange();
range.Minimum = new Spin(tj_min / 2.0);
range.Maximum = new Spin(tj_max / 2.0);
return (range);
}
private static Spin[] AllSpinsInRange(SpinRange range)
{
int tj_min = (int) Math.Round(2 * range.Minimum.J);
int tj_max = (int) Math.Round(2 * range.Maximum.J);
List<Spin> spins = new List<Spin>();
for (int tj = tj_min; tj <= tj_max; tj+=2) {
spins.Add(new Spin(tj / 2.0));
}
return (spins.ToArray());
}
private static Spin[] RandomSpinsInRange(SpinRange range, int n)
{
int tj_min = (int) Math.Truncate(2.0 * range.Minimum.J);
int tj_max = (int) Math.Truncate(2.0 * range.Maximum.J);
Spin[] spins = new Spin[n];
Random rng = new Random(1);
for (int i = 0; i < n; i++) {
spins[i] = new Spin((tj_min + 2 * rng.Next((tj_max - tj_min) / 2 + 1))/2.0);
}
return (spins);
}
