/**
* The implementation of the inverse error function.
* @param p
* @param q
* @param s
* @return
*/
private static double erfInvImpl(double p, double q, double s)
{
double result;
if (p <= 0.5)
{
float y = 0.0891314744949340820313f;
double g = p * (p + 10);
double r = Evaluate.polynomial(p, Coefficients.ervInvImpAn) / Evaluate.polynomial(p, Coefficients.ervInvImpAd);
result = (g * y) + (g * r);
}
else if (q >= 0.25)
{
float y = 2.249481201171875f;
double g = MathFunctions.sqrt(-2 * MathFunctions.ln(q));
double xs = q - 0.25;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpBn) / Evaluate.polynomial(xs, Coefficients.ervInvImpBd);
result = g / (y + r);
}
else
{
double x = MathFunctions.sqrt(-MathFunctions.ln(q));
if (x < 3)
{
float y = 0.807220458984375f;
double xs = x - 1.125;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpCn) / Evaluate.polynomial(xs, Coefficients.ervInvImpCd);
result = (y * x) + (r * x);
}
else if (x < 6)
{
float y = 0.93995571136474609375f;
double xs = x - 3;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpDn) / Evaluate.polynomial(xs, Coefficients.ervInvImpDd);
result = (y * x) + (r * x);
}
else if (x < 18)
{
float y = 0.98362827301025390625f;
double xs = x - 6;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpEn) / Evaluate.polynomial(xs, Coefficients.ervInvImpEd);
result = (y * x) + (r * x);
}
else if (x < 44)
{
float y = 0.99714565277099609375f;
double xs = x - 18;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpFn) / Evaluate.polynomial(xs, Coefficients.ervInvImpFd);
result = (y * x) + (r * x);
}
else
{
float y = 0.99941349029541015625f;
double xs = x - 44;
double r = Evaluate.polynomial(xs, Coefficients.ervInvImpGn) / Evaluate.polynomial(xs, Coefficients.ervInvImpGd);
result = (y * x) + (r * x);
}
}
return(s * result);
}
/**
* 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);
}