internal static LPhiObject LPhi(double[] z)
{
//# z: can be scalar or vector
LPhiObject rep = new LPhiObject(z.Length);
/*
* lphi <- function(z)
* {
# z: can be scalar or vector
#
# log.phi <- dnorm(z, log=T) # log(phi(z))
# log.Phi <- pnorm(z, log.p=T) # log(Phi(z))
#
# r <- exp(log.phi-log.Phi) # phi(z)/Phi(z)
# r2 <- exp(2*(log.phi-log.Phi)) # phi^2(z) / Phi^2 (z)
#
# list(r=r, r2=r2) # r and r2 are of same length as z
# } # end of lphi
*/
double[] tmp = NormalDistribution.DNorm(z, give_log: true).Substract(NormalDistribution.PNorm(z, log_p: true));
rep.R = tmp.Exp(); // phi(z)/Phi(z)
rep.R2 = tmp.Multiply(2).Exp(); // phi^2(z) / Phi^2 (z)
return(rep);
}
internal override double[] Start(SGNFnAParam A)
{
double s0 = Math.Sqrt(2 * A.B / A.N);
double g0 = NormalDistribution.PNorm(A.Mu / s0, log_p: true);
double gp0 = -NormalDistribution.DNorm(A.Mu / s0) * A.Mu / Math.Pow(s0, 2) / NormalDistribution.PNorm(A.Mu / s0);
double c3 = A.N * (gp0 - 1);
double c2 = A.N * (1 - g0 + gp0 * s0);
double c0 = -A.B;
double[] theta = Tools.Combine(c0, 0, c2, c3);
double[] roots = Numerics.CubicEquation.GetRealRoots(theta, l: 0).ToArray();
if (roots.Length == 0)
{
roots = Tools.Combine(s0);
}
return(roots);
}
