public static double[][] NormalCdfRatioTable2(int nSteps, int nMax, int nTerms, double start, double step)
{
double[][] table = new double[nSteps + 1][];
double[] derivs = new double[nMax + nSteps * nTerms];
for (int n = 0; n < derivs.Length; n++)
{
//Console.WriteLine("ncdfmr({0}) = {1}", n, NormalCdfMomentRatioConFrac(n, start));
derivs[n] = MMath.NormalCdfMomentRatioConFrac(n, start);
//Console.WriteLine("derivs[{0}] = {1}", n, derivs[n]);
}
table[0] = derivs;
for (int i = 0; i < nSteps; i++)
{
int nMax2 = derivs.Length - nTerms;
Console.WriteLine("{0} nMax2 = {1}", i, nMax2);
double[] newDerivs = new double[nMax2];
for (int n = 0; n < nMax2; n++)
{
newDerivs[n] = MMath.NormalCdfMomentRatioTaylor(n, step, derivs);
}
table[i + 1] = newDerivs;
derivs = newDerivs;
}
return(table);
}
public static void NormalCdfRatioTest2()
{
// larger n requires more terms in the Taylor expansion
// need nTerms=60 to get n=19, x=-4 from x=-8
// nTerms=40 can do it in 2 steps, even though the 60 values for x=-6 are not accurate
// (n=19,x=-4) in 4 steps: nTerms=30
// (n=19,x=-4) in 1 step from x=-6: nTerms=100
// thus it makes a difference where you start from
double start = -6;
double step = 2;
double[][] table = NormalCdfRatioTable2(1, 20, 100, start, step);
double x = start;
for (int i = 0; i < table.Length; i++)
{
for (int j = 0; j < table[i].Length; j++)
{
double r = MMath.NormalCdfMomentRatioConFrac(j, x);
Console.WriteLine("({0},{1}) error = {2}", j, x, Math.Abs(table[i][j] - r) / r);
}
x += step;
}
}
public static void NormalCdfRatioTest3()
{
// x=-2,-4,-8 are good positions for Taylor expansion
double x = -4;
for (int i = 0; i < 100; i++)
{
// x=-10: nBase=20,30 is unusually good, nBase=50 doesn't work as well
// x=-20: nBase=50 works well
// larger x allows larger nBase
// x=-8: nBase=100
// x=-6: nBase=10 works well
// x=-5: poor
// x=-4: nBase=40
// x=-3: poor results for any nBase
// x=-2: nBase=100 works well
double r2 = MMath.NormalCdfMomentRatioRecurrence2(i, x, 100);
double r = MMath.NormalCdfMomentRatioConFrac(i, x);
//Console.WriteLine("recurrence = {0}, confrac = {1}", r1, r2);
//Console.WriteLine("ncdfmr = {0}, ncdfmr/(i-1)!! = {1}", r, r/DoubleFact(i-1));
//Console.WriteLine("ncdfmr = {0}, ncdfmr*i! = {1}", r, r*MMath.Gamma(i+1));
Console.WriteLine("error = {0}", Math.Abs(r - r2) / Math.Abs(r));
}
}
