//steffensen's method
public static double FindRoot(ProbabilityFunction func, double xGuess)
{
double[] xvals = new double[iterations];
double funcResult1;
double funcResult2;
double deltaSquare;
xvals[0] = xGuess;
for (int i = 0; i < iterations - 1; i++)
{
funcResult1 = func(xvals[i]);
funcResult2 = func(funcResult1);
deltaSquare = xvals[i] - (Math.Pow((funcResult2 - xvals[i]), 2) / (funcResult2 - (2 * funcResult1) + xvals[i])); //aitkens delta square method
if (Math.Abs(deltaSquare - xvals[i]) < tolerance) //close enough
{
return(deltaSquare);
}
xvals[i + 1] = deltaSquare;
//xvals[i + 1] = xvals[i] - (funcResult / (((func(xvals[i] + funcResult) - funcResult) / (funcResult))));
}
return(xvals[iterations - 1]);
}
public Ziggurat(PDFType pdfType)
{
pdf = new PDF(0, 1);
switch (pdfType)
{
case PDFType.Normal:
pFunc = pdf.NormalPDF;
lowerBound = 0;
upperBound = 0x100000000;
guess = 3.56;
tailBound = 10;
break;
case PDFType.Laplace:
pFunc = pdf.LaplacePDF;
lowerBound = 0;
upperBound = 5000;
guess = 9;
tailBound = 10;
break;
case PDFType.T:
pFunc = pdf.TPDF;
lowerBound = 0;
upperBound = Int16.MaxValue;
guess = 4;
tailBound = 10;
break;
}
GenerateZigTable();
}
public static double Integrate(ProbabilityFunction f, double lower, double upper, double intervals)
{
double h = (upper - lower) / intervals;
double res = (f(lower) + f(upper)) / 2;
for (int i = 1; i < intervals; i++)
{
res += f(lower + i * h);
}
return(h * res);
}
//my guess method
public static double FindGuess(ProbabilityFunction func, double guess, double sanity)
{
double increment = .1;
double current;
double update;
bool changeInc = false;
bool increased = false;
for (int i = 0; i < iterations; i++)
{
current = func(guess);
if (changeInc)
{
increment = increment / 10;
changeInc = false;
}
if (Math.Abs(current - sanity) < tolerance)
{
return(guess);
}
if (current > sanity)
{
guess += increment;
increased = true;
}
else if (current < sanity)
{
guess -= increment;
increased = false;
}
update = func(guess);
if ((Math.Abs(current - sanity) < Math.Abs(update - sanity)))
{
if (increased)
{
guess -= increment;
changeInc = true;
}
else
{
guess += increment;
changeInc = true;
}
}
}
return(guess);
}
private static void CheckPearsonCriteria(List <double> list, ProbabilityFunction function, int criteriaItemsAmount)
{
var probabilityFunctionValues = GetProbabilityFunctionValues();
var valuesAmount = GetAmountByValues();
double value = 0;
for (int i = 0; i < criteriaItemsAmount; i++)
{
if (probabilityFunctionValues[i] != 0)
{
value += Math.Pow(valuesAmount[i] - N * probabilityFunctionValues[i], 2) / (N * probabilityFunctionValues[i]);
}
}
Console.WriteLine($"Pearson criterion: {DisplayCriteriaResults(Pearson0_05Quantiles[criteriaItemsAmount - 1])}");
List <double> GetProbabilityFunctionValues() //For Puasson: 0.220, 0.333, 0.252, 0.127, 0.048, 0.015, 0.005
{
return(GetIEnumerableProbabilityFunctionValues().ToList());
IEnumerable <double> GetIEnumerableProbabilityFunctionValues()
{
for (int i = 0; i < criteriaItemsAmount; i++)
{
yield return(function(i));
}
}
}
List <int> GetAmountByValues()
{
return(GetIEnumerableAmountByValues().ToList());
IEnumerable <int> GetIEnumerableAmountByValues()
{
for (int i = 0; i < criteriaItemsAmount; i++)
{
yield return(list.Count(x => x == i));
}
}
}
string DisplayCriteriaResults(double quantile) => value < quantile ?
$"{value:F5} < {quantile:F3}, so it's passed" : $"{value:F5} > {quantile:F3}, so it isn't passed";
}
private static void DisplayResults(string parameters, int criteriaItemsAmount, List <double> results,
ProbabilityFunction probabilityFunction, MathematicalExpectation mathematicalExpectation, Dispersion dispersion)
{
Console.WriteLine(Environment.NewLine +
$"-----{dispersion.Method.Name.Replace("Dispersion", "")} distribution ({parameters})-----");
results.Take(30).ToList().ForEach(x => Console.Write($"{x:F0} "));
Console.Write(Environment.NewLine + $"{N} items: ");
for (int i = 0; i < Math.Min(7, criteriaItemsAmount); i++)
{
Console.Write($"{i}({results.Count(x => x == i)}) ");
}
Console.WriteLine();
Console.WriteLine($"Practical : Average={results.Average():F5}, Dispersion={CalculateDispersion(results.ToList()):F5}");
Console.WriteLine($"Theoretical: Average={mathematicalExpectation():F5}, Dispersion={dispersion():F5}");
CheckPearsonCriteria(GetSortedList(results), probabilityFunction, criteriaItemsAmount);
double CalculateDispersion(List <double> list) => list.Sum(x => Math.Pow(x - list.Average(), 2)) / list.Count;
List <double> GetSortedList(List <double> list) => list.OrderBy(x => x).ToList();
}
//brent's method
public static double Root(ProbabilityFunction func, double lowerBound, double upperBound)
{
double a = lowerBound;
double b = upperBound;
double c;
double fa = func(a);
double fb = func(b);
double fc;
double fs = 0;
double s = 0;
double d = 0;
bool flag = true;
if ((fa * fb) >= 0)
{
return(0);
}
if (Math.Abs(fa) < Math.Abs(fb)) //swap if the magnitude of lower is less then upper
{
var temp = a;
a = b;
b = temp;
temp = fa;
fa = fb;
fb = temp;
}
fc = fa;
c = a;
for (int i = 0; i < iterations; i++)
{
if (Math.Abs(b - a) < tolerance)
{
return(s);
}
if (fa != fc && fb != fc) //inverse quadratic interpolation
{
s = (a * fb * fc / ((fa - fb) * (fa - fc))) + (b * fa * fc / ((fb - fa) * (fb - fc))) + (c * fa * fb / ((fc - fa) * (fc - fb)));
}
else //secant
{
s = b - fb * (b - a) / (fb - fa);
}
//bijection
if (((s < (3 * a + b) * 0.25) || (s > b)) ||
(flag && (Math.Abs(s - b) >= (Math.Abs(b - c) / 2))) ||
(flag == false && (Math.Abs(s - b) >= (Math.Abs(c - d) / 2))) ||
(flag && (Math.Abs(b - c) < tolerance)) ||
(flag == false && (Math.Abs(c - d) < tolerance)))
{
s = (a + b) / 2;
flag = true;
}
else
{
flag = false;
}
fs = func(s);
d = c;
c = b;
fc = fb;
if (fa * fs < 0)
{
b = s;
fb = fs;
}
else
{
a = s;
fa = fs;
}
if (Math.Abs(fa) < Math.Abs(fb))
{
var temp = a;
a = b;
b = temp;
temp = fa;
fa = fb;
fb = temp;
}
}
return(0);
}
