/**
* Real valued log gamma function.
* @param x
* @return Returns log value from gamma function.
*/
public static double logGamma(double x)
{
if (Double.IsNaN(x))
{
return(Double.NaN);
}
if (Double.IsPositiveInfinity(x))
{
return(Double.PositiveInfinity);
}
if (Double.IsNegativeInfinity(x))
{
return(Double.NaN);
}
if (MathFunctions.isInteger(x))
{
if (x >= 0)
{
return(MathFunctions.ln(Math.Abs(gammaInt((long)(Math.Round(x))))));
}
else
{
return(MathFunctions.ln(Math.Abs(gammaInt(-(long)(Math.Round(-x))))));
}
}
double p, q, w, z;
if (x < -34.0)
{
q = -x;
w = logGamma(q);
p = Math.Floor(q);
if (p == q)
{
return(Double.NaN);
}
z = q - p;
if (z > 0.5)
{
p += 1.0;
z = p - q;
}
z = q * Math.Sin(Math.PI * z);
if (z == 0.0)
{
return(Double.NaN);
}
z = MathConstants.LNPI - Math.Log(z) - w;
return(z);
}
if (x < 13.0)
{
z = 1.0;
while (x >= 3.0)
{
x -= 1.0;
z *= x;
}
while (x < 2.0)
{
if (x == 0.0)
{
return(Double.NaN);
}
z /= x;
x += 1.0;
}
if (z < 0.0)
{
z = -z;
}
if (x == 2.0)
{
return(Math.Log(z));
}
x -= 2.0;
p = x * Evaluate.polevl(x, Coefficients.logGammaB, 5) / Evaluate.p1evl(x, Coefficients.logGammaC, 6);
return(Math.Log(z) + p);
}
if (x > 2.556348e305)
{
return(Double.NaN);
}
q = (x - 0.5) * Math.Log(x) - x + 0.91893853320467274178;
if (x > 1.0e8)
{
return(q);
}
p = 1.0 / (x * x);
if (x >= 1000.0)
{
q += ((7.9365079365079365079365e-4 * p - 2.7777777777777777777778e-3) * p + 0.0833333333333333333333) / x;
}
else
{
q += Evaluate.polevl(p, Coefficients.logGammaA, 4) / x;
}
return(q);
}
/**
* Calculates the inverse error function evaluated at x.
* @param x
* @param invert
* @return
*/
private static double erfImp(double z, bool invert)
{
if (z < 0)
{
if (!invert)
{
return(-erfImp(-z, false));
}
if (z < -0.5)
{
return(2 - erfImp(-z, true));
}
return(1 + erfImp(-z, false));
}
double result;
if (z < 0.5)
{
if (z < 1e-10)
{
result = (z * 1.125) + (z * 0.003379167095512573896158903121545171688);
}
else
{
result = (z * 1.125) + (z * Evaluate.polynomial(z, Coefficients.erfImpAn) / Evaluate.polynomial(z, Coefficients.erfImpAd));
}
}
else if ((z < 110) || ((z < 110) && invert))
{
invert = !invert;
double r, b;
if (z < 0.75)
{
r = Evaluate.polynomial(z - 0.5, Coefficients.erfImpBn) / Evaluate.polynomial(z - 0.5, Coefficients.erfImpBd);
b = 0.3440242112F;
}
else if (z < 1.25)
{
r = Evaluate.polynomial(z - 0.75, Coefficients.erfImpCn) / Evaluate.polynomial(z - 0.75, Coefficients.erfImpCd);
b = 0.419990927F;
}
else if (z < 2.25)
{
r = Evaluate.polynomial(z - 1.25, Coefficients.erfImpDn) / Evaluate.polynomial(z - 1.25, Coefficients.erfImpDd);
b = 0.4898625016F;
}
else if (z < 3.5)
{
r = Evaluate.polynomial(z - 2.25, Coefficients.erfImpEn) / Evaluate.polynomial(z - 2.25, Coefficients.erfImpEd);
b = 0.5317370892F;
}
else if (z < 5.25)
{
r = Evaluate.polynomial(z - 3.5, Coefficients.erfImpFn) / Evaluate.polynomial(z - 3.5, Coefficients.erfImpFd);
b = 0.5489973426F;
}
else if (z < 8)
{
r = Evaluate.polynomial(z - 5.25, Coefficients.erfImpGn) / Evaluate.polynomial(z - 5.25, Coefficients.erfImpGd);
b = 0.5571740866F;
}
else if (z < 11.5)
{
r = Evaluate.polynomial(z - 8, Coefficients.erfImpHn) / Evaluate.polynomial(z - 8, Coefficients.erfImpHd);
b = 0.5609807968F;
}
else if (z < 17)
{
r = Evaluate.polynomial(z - 11.5, Coefficients.erfImpIn) / Evaluate.polynomial(z - 11.5, Coefficients.erfImpId);
b = 0.5626493692F;
}
else if (z < 24)
{
r = Evaluate.polynomial(z - 17, Coefficients.erfImpJn) / Evaluate.polynomial(z - 17, Coefficients.erfImpJd);
b = 0.5634598136F;
}
else if (z < 38)
{
r = Evaluate.polynomial(z - 24, Coefficients.erfImpKn) / Evaluate.polynomial(z - 24, Coefficients.erfImpKd);
b = 0.5638477802F;
}
else if (z < 60)
{
r = Evaluate.polynomial(z - 38, Coefficients.erfImpLn) / Evaluate.polynomial(z - 38, Coefficients.erfImpLd);
b = 0.5640528202F;
}
else if (z < 85)
{
r = Evaluate.polynomial(z - 60, Coefficients.erfImpMn) / Evaluate.polynomial(z - 60, Coefficients.erfImpMd);
b = 0.5641309023F;
}
else
{
r = Evaluate.polynomial(z - 85, Coefficients.erfImpNn) / Evaluate.polynomial(z - 85, Coefficients.erfImpNd);
b = 0.5641584396F;
}
double g = MathFunctions.exp(-z * z) / z;
result = (g * b) + (g * r);
}
else
{
result = 0;
invert = !invert;
}
if (invert)
{
result = 1 - result;
}
return(result);
}