private double HigherLocalMax(GenObject o, SGNFnAParam A, double dipX, double[] range, double epsilon)
{
//# Find a starting point on each side of dip.x
double[] start = o.Start(A);
double tmp = start.Substract(dipX).Abs().Max();
double startLeft = start.Min();
if (startLeft > dipX)
{
startLeft = dipX - tmp;
}
double startRight = start.Max();
if (startRight < dipX)
{
startRight = dipX + tmp;
}
//# Look for starting points with negative values for h''
//# i) on left side
bool cntn = o.LogFSecond(startLeft, A) > 0;
while (cntn)
{
startLeft = startLeft - tmp;
if (startLeft < range[0])
{
startLeft = (range[0] + startLeft + tmp) / 2;
}
cntn = o.LogFSecond(startLeft, A) > 0;
}
//# ii) on right side
cntn = o.LogFSecond(startRight, A) > 0;
while (cntn)
{
startRight = startRight + tmp;
cntn = o.LogFSecond(startRight, A) > 0;
}
//# Run pure Newton-Raphson to find local max on each side
//# i) left side
double x = startLeft;
cntn = true;
double hp = o.LogFPrime(x, A);
while (cntn)
{
double change = hp / o.LogFSecond(x, A);
x = x - change;
hp = o.LogFPrime(x, A);
cntn = Math.Abs(hp) > epsilon;
}
double localModeLeft = x;
//# ii) right-side
x = startRight;
cntn = true;
hp = o.LogFPrime(x, A);
while (cntn)
{
double change = hp / o.LogFSecond(x, A);
x = x - change;
hp = o.LogFPrime(x, A);
cntn = Math.Abs(hp) > epsilon;
}
double localModeRight = x;
double hLeft = o.LogF(localModeLeft, A);
double hRight = o.LogF(localModeRight, A);
x = hLeft > hRight ? localModeLeft : localModeRight;
return(x);
} //# end of higher.local.max
} //# end of split.starting.values.leftRight
//# new_0.11
private MaxFastTrackObject MaxFastTrack(GenObject o, SGNFnAParam A, double lowerLimit, double rightsideX, double rightsideHp, double epsilon = 1e-4, double epsilonX = 1e-20)
{
double x = rightsideX;
double h = o.LogF(x, A);
double hp = rightsideHp;
//b = list(x = c(NA, x), h = c(NA, h), hp = c(NA, hp))
double[] bX = new double[2] {
x, Tools.NA
};
double[] bH = new double[2] {
h, Tools.NA
};
double[] bHp = new double[2] {
hp, Tools.NA
};
x = (x + lowerLimit) / 2;
bool cntn = true;
//# Find a point with positive slope (that is, to the left of the mode)
while (cntn)
{
hp = o.LogFPrime(x, A);
if (hp > 0)
{
cntn = double.IsInfinity(hp);
if (cntn)
{
double nextX = (3 * x - lowerLimit) / 2.0;
lowerLimit = x;
cntn = Math.Abs(nextX - x) > epsilonX;
if (cntn)
{
x = nextX;
}
}
}
else
{
x = (x + lowerLimit) / 2.0;
}
}
hp = o.LogFPrime(x, A);
bool converged = Tools.IsFinite(hp) & (hp > 0);
cntn = converged;
while (cntn)
{
int side = hp > 0 ? 0 : 1;
bX[side] = x;
bH[side] = o.LogF(x, A);
bHp[side] = hp;
double bDiff = bHp.Diff()[0];
if (bDiff == 0)
{
x = bX.Mean();
}
else
{
x = (bHp.Multiply(bX).Diff()[0] - bH.Diff()[0]) / bDiff;
if ((x <= bX[0]) || (x >= bX[1]))
{
x = bX.Mean();
}
hp = o.LogFPrime(x, A);
cntn = Math.Abs(hp) > epsilon;
}
}
h = o.LogF(x, A);
return(new MaxFastTrackObject(x, h, converged));
} //# end of max.fastTrack
