internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
double D = -A.B;
double B = -A.N * (Math.Log(A.Mode) - 1.0) - target;
double qA = -A.N / A.Mode;
roots.AddRange(CubicEquation.GetRealRoots(Util.Tools.Combine(D, 0, B, qA), l: 0, u: A.Mode, ROrder: true));// # modif_0.11
roots.Add(Math.Exp(Math.Log(2.0) - target / A.N));
return(roots);
}
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
double c3 = -A.N;
double c2 = A.N - target;
double c0 = -A.B;
roots.AddRange(CubicEquation.GetRealRoots(Tools.Combine(c0, 0, c2, c3), l: 0));
roots.Add(-target / A.N);
return(roots);
} //# end of log.f.inv.remote
internal override double[] Start(SGNFnAParam A)
{
List <double> roots = new List <double>();
//# solutions in small values for t
double C = A.Y2 / A.CV2;
double B = -A.Y / A.CV2;
roots.AddRange(QuadraticEquation.GetRealRoots(Tools.Combine(C, B, -1), l: 0, ROrder: true));
//# solutions in large values for t
double D = A.Y / A.CV2;
B = -A.Mu / A.Sigma2;
double qA = 1 / A.Sigma2;
double[] theta = Tools.Combine(D, 1, B, qA);
roots.AddRange(CubicEquation.GetRealRoots(theta, l: 0, ROrder: true));
return(roots.ToArray());
} //# end of start
} //LogFSecond
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
//# small values
double c3 = -(A.N + 1.0) + A.LM / A.LS2;
double c2 = A.N + 1 - Math.Pow(A.LM, 2) / 2.0 / A.LS2 - target;
double c0 = -A.B;
roots.AddRange(CubicEquation.GetRealRoots(Tools.Combine(c3, c2, 0, c0), l: 0));
//# large values
double C = -Math.Pow(A.LM, 2) / 2.0 / A.LS2 - target;
double B = A.LM / A.LS2 - (A.N + 1);
double vA = -1.0 / 2.0 / A.LS2;
double[] tmp = QuadraticEquation.GetRealRoots(Tools.Combine(C, B, vA), l: 0, ROrder: true).ToArray().Exp();
roots.AddRange(tmp);
return(roots);
} //LogFInvRemote
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
roots.Add(A.Y / (1 + Math.Sqrt(-2.0 * A.CV2 * target)));
//# We try a solution with a small t
double D = -A.Y2 / 2.0 / A.CV2;
double C = A.Y / A.CV2;
/*
* 3/2 - 1/2/A$cv2 - A$mu^2/2/A$sigma2 - target
*/
double B =
3.0 / 2.0
- 1.0 / 2.0 / A.CV2
- Math.Pow(A.Mu, 2) / 2.0 / A.Sigma2
- target;
double qA = -2.0 + A.Mu / A.Sigma2;
double[] theta = Tools.Combine(D, C, B, qA);
roots.AddRange(CubicEquation.GetRealRoots(theta, ROrder: true));
// Look also for a solution with a large value for t
double tmp = -2.0 * A.Sigma2 * (target + 1 / 2.0 / A.CV2);
if (tmp > 0)
{
double racine = A.Mu + Math.Sqrt(tmp);
if (racine > 0.0)
{
roots.Add(racine);
}
}
return(roots);
}
