/// <summary>
/// Computes the cumulative distribution function of the distribution.
/// </summary>
/// <param name="x">The location at which to compute the cumulative density.</param>
/// <returns>the cumulative density at <paramref name="x"/>.</returns>
public double CumulativeDistribution(double x)
{
int alpha = Minimum;
int beta = Maximum;
if (x <= alpha)
{
return(0.0);
}
if (x > beta)
{
return(1.0);
}
var sum = 0.0;
var k = (int)Math.Ceiling(x - alpha) - 1;
for (var i = alpha; i <= alpha + k; i++)
{
sum += SpecialFunctions.Binomial(_m, i) * SpecialFunctions.Binomial(_populationSize - _m, _n - i);
}
return(sum / SpecialFunctions.Binomial(_populationSize, _n));
}
/// <summary>
/// 분포의 확률
/// </summary>
/// <param name="k">시도 횟수</param>
/// <returns></returns>
public double Probability(int k)
{
if (k < 0)
{
return(0.0);
}
if (k > _n)
{
return(0.0);
}
if (_p.ApproximateEqual(0.0) && k == 0)
{
return(1.0);
}
if (_p.ApproximateEqual(0.0))
{
return(0.0);
}
if (_p.ApproximateEqual(1.0) && k == _n)
{
return(1.0);
}
if (_p.ApproximateEqual(1.0))
{
return(0.0);
}
return(SpecialFunctions.Binomial(_n, k) * Math.Pow(_p, k) * Math.Pow(1.0 - _p, _n - k));
}
/// <summary>
/// Computes the probability mass (PMF) at k, i.e. P(X = k).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
/// <returns>the probability mass at location <paramref name="k"/>.</returns>
public double Probability(int k)
{
if (k < 0)
{
return(0.0);
}
if (k > _trials)
{
return(0.0);
}
if (_p == 0.0 && k == 0)
{
return(1.0);
}
if (_p == 0.0)
{
return(0.0);
}
if (_p == 1.0 && k == _trials)
{
return(1.0);
}
if (_p == 1.0)
{
return(0.0);
}
return(SpecialFunctions.Binomial(_trials, k) * Math.Pow(_p, k) * Math.Pow(1.0 - _p, _trials - k));
}
static void Main(string[] args)
{
// 1. Calcula o coeficiente binonmial
Console.WriteLine("1. Calcular o coeficiente binomial ");
while (true)
{
Console.WriteLine("Informe um número de 1 a 100 ( 999 -> Sai )");
string input = Console.ReadLine();
int n;
if (Int32.TryParse(input, out n))
{
if (n == 999)
{
break;
}
Console.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N"));
Console.WriteLine();
}
else
{
Console.WriteLine("Valor inválido...");
}
}
Console.WriteLine("Pressione algo para encerrar...");
Console.ReadLine();
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Factorial">Factorial</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Binomial_coefficient">Binomial coefficient</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</seealso>
public void Run()
{
// 1. Compute the factorial of 5
Console.WriteLine(@"1. Compute the factorial of 5");
Console.WriteLine(SpecialFunctions.Factorial(5).ToString("N"));
Console.WriteLine();
// 2. Compute the logarithm of the factorial of 5
Console.WriteLine(@"2. Compute the logarithm of the factorial of 5");
Console.WriteLine(SpecialFunctions.FactorialLn(5).ToString("N"));
Console.WriteLine();
// 3. Compute the binomial coefficient: 10 choose 8
Console.WriteLine(@"3. Compute the binomial coefficient: 10 choose 8");
Console.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N"));
Console.WriteLine();
// 4. Compute the logarithm of the binomial coefficient: 10 choose 8
Console.WriteLine(@"4. Compute the logarithm of the binomial coefficient: 10 choose 8");
Console.WriteLine(SpecialFunctions.BinomialLn(10, 8).ToString("N"));
Console.WriteLine();
// 5. Compute the multinomial coefficient: 10 choose 2, 3, 5
Console.WriteLine(@"5. Compute the multinomial coefficient: 10 choose 2, 3, 5");
Console.WriteLine(SpecialFunctions.Multinomial(10, new[] { 2, 3, 5 }).ToString("N"));
Console.WriteLine();
}
/// <summary>
/// Computes the probability mass (PMF) at k, i.e. P(X = k).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
/// <param name="population">The size of the population (N).</param>
/// <param name="success">The number successes within the population (K, M).</param>
/// <param name="draws">The number of draws without replacement (n).</param>
/// <returns>the probability mass at location <paramref name="k"/>.</returns>
public static double PMF(int population, int success, int draws, int k)
{
//if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population)) {
// throw new ArgumentException("InvalidDistributionParameters");
//}
return(SpecialFunctions.Binomial(success, k) * SpecialFunctions.Binomial(population - success, draws - k) / SpecialFunctions.Binomial(population, draws));
}
public void ValidateProbability(
[Values(0, 1, 2, 2, 2, 10, 10, 10, 10)] int size,
[Values(0, 1, 1, 1, 2, 1, 1, 5, 5)] int m,
[Values(0, 1, 1, 1, 2, 1, 1, 3, 3)] int n,
[Values(0, 1, 0, 1, 2, 0, 1, 1, 3)] int x)
{
var d = new Hypergeometric(size, m, n);
Assert.AreEqual(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(size - m, n - x) / SpecialFunctions.Binomial(size, n), d.Probability(x));
}
public void CanComputeBinomial()
{
AssertHelpers.AlmostEqualRelative(1, SpecialFunctions.Binomial(1, 1), 14);
AssertHelpers.AlmostEqualRelative(10, SpecialFunctions.Binomial(5, 2), 14);
AssertHelpers.AlmostEqualRelative(35, SpecialFunctions.Binomial(7, 3), 14);
AssertHelpers.AlmostEqualRelative(1, SpecialFunctions.Binomial(1, 0), 14);
AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(0, 1), 14);
AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(5, 7), 14);
AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(5, -7), 14);
}
public static Prediction GetSymmetricPrediction(double spotPrice, double volatility, double interestRate, double daysInFuture, int?numberOfPointsArg = null)
{
int numberOfPoints = numberOfPointsArg ?? DefaultNumberOfPredictionResults;
volatility = 0.2;
double t = daysInFuture / (365 * numberOfPoints);
double tmp = interestRate / 100 - volatility * volatility / 2;
double x = Math.Sqrt(tmp * tmp * t * t + volatility * volatility * t);
double probabilityUp = x.AlmostEqual(0)
? 0.5 + tmp / 2
: 0.5 + (tmp * t) / (2 * x);
double probabilityDown = 1 - probabilityUp;
double[] stockPrice = new double[numberOfPoints];
double[] cumulativeProb = new double[numberOfPoints];
double prevStockPrice = stockPrice[0] = Math.Log(spotPrice) - (numberOfPoints) * x;
for (int i = 0; i < numberOfPoints; i++)
{
prevStockPrice = prevStockPrice + 2 * x;
stockPrice[i] = Math.Exp(prevStockPrice);
}
stockPrice[0] = Math.Exp(stockPrice[0]);
double prevCumulativeProb = 0.0;
for (int i = 0; i < numberOfPoints; i++)
{
double probability = SpecialFunctions.Binomial(numberOfPoints, i) *
Math.Pow(probabilityDown, numberOfPoints - i) *
Math.Pow(probabilityUp, i);
probability += prevCumulativeProb;
cumulativeProb[i] = probability.CoerceZero(SignificantDoubleValue);
prevCumulativeProb = probability;
}
for (int i = numberOfPoints / 2; i < numberOfPoints; i++)
{
cumulativeProb[i] = 1.0 - cumulativeProb[i];
if (cumulativeProb[i] < 0)
{
cumulativeProb[i] = 0;
}
}
Prediction prediction = new Prediction(cumulativeProb, stockPrice, daysInFuture);
return(prediction);
}
/// <summary> Gets possible lots. </summary>
/// <remarks> superreeen, 09.11.2013. </remarks>
/// <returns> The possible lots. </returns>
//private static List<PossibleLot> GetPossibleLots()
//{
// List<PossibleLot> findings = new List<PossibleLot>();
// decimal gain = 1;
// decimal raiser = 1;
// decimal totalGain = 0;
// decimal gainStepAllocate = 0;
// decimal gainAllocate = 0;
// for (int n = 5; n >= 0; n--)
// {
// gainAllocate = (gain * (n)) / (n + raiser);
// gain -= gainAllocate;
// for (int s = 2; s >= 0; s--)
// {
// gainStepAllocate = (gainAllocate * (s + 2)) / (s + raiser + 2);
// gainAllocate -= gainStepAllocate;
// totalGain += gainStepAllocate;
// raiser += 2;
// findings.Add(new PossibleLot()
// {
// Numbers = n,
// Stars = s,
// Probability = (decimal)(SpecialFunctions.Binomial(Numbers, n)
// * SpecialFunctions.Binomial(MaxNumbers - Numbers, Numbers - n)
// / SpecialFunctions.Binomial(MaxNumbers, Numbers)
// * SpecialFunctions.Binomial(Stars, s)
// * SpecialFunctions.Binomial(MaxStars - Stars, Stars - s)
// / SpecialFunctions.Binomial(MaxStars, Stars)),
// Gain = gainStepAllocate
// });
// }
// }
// return findings;
//}
private static List <PossibleLot> GetPossibleLots()
{
// key numbers & stars
Dictionary <int, decimal> distribution = new Dictionary <int, decimal>();
distribution[52] = 0.300m;
distribution[51] = 0.080m;
distribution[50] = 0.020m;
distribution[42] = 0.020m;
distribution[41] = 0.010m;
distribution[40] = 0.006m;
distribution[32] = 0.006m;
distribution[31] = 0.004m;
distribution[30] = 0.002m;
distribution[22] = 0.002m;
distribution[21] = 0.040m;
distribution[20] = 0.070m;
distribution[12] = 0.090m;
distribution[11] = 0.090m;
distribution[10] = 0.110m;
distribution[02] = 0.000m;
distribution[01] = 0.000m;
distribution[00] = 0.000m;
List <PossibleLot> findings = new List <PossibleLot>();
for (int n = 5; n >= 0; n--)
{
for (int s = 2; s >= 0; s--)
{
findings.Add(new PossibleLot()
{
Numbers = n,
Stars = s,
Probability = (decimal)(SpecialFunctions.Binomial(Numbers, n)
* SpecialFunctions.Binomial(MaxNumbers - Numbers, Numbers - n)
/ SpecialFunctions.Binomial(MaxNumbers, Numbers)
* SpecialFunctions.Binomial(Stars, s)
* SpecialFunctions.Binomial(MaxStars - Stars, Stars - s)
/ SpecialFunctions.Binomial(MaxStars, Stars)),
Gain = distribution[(n * 10) + s]
});
}
}
return(findings);
}
// These are the two-sided coefficients, so not much use.
private DenseVector TwoSidedCoefficients(int N)
{
if (N % 2 == 0)
{
throw new Exception("Error, FilterLength must be odd!");
}
int m = (int)(0.5 * (N - 3));
int M = (int)(0.5 * (N - 1));
double denominator = 1 / (Math.Pow(2, 2 * m + 1));
double[] coeff = new double[M];
for (int k = 0; k < M; ++k)
{
coeff[k] = (SpecialFunctions.Binomial(2 * m, m - k + 1) - SpecialFunctions.Binomial(2 * m, m - k - 1)) * denominator;
}
return(new DenseVector(coeff));
}
/// <summary>
///
/// </summary>
public List <Finding> getFindings()
{
List <Finding> findings = new List <Finding>();
double gain = 1;
double raiser = 1;
double totalGain = 0;
double gainStepAllocate = 0;
double gainAllocate = 0;
for (int n = 5; n >= 0; n--)
{
gainAllocate = (gain * (n)) / (n + raiser);
gain -= gainAllocate;
for (int s = 2; s >= 0; s--)
{
gainStepAllocate = (gainAllocate * (s + 2)) / (s + raiser + 2);
gainAllocate -= gainStepAllocate;
totalGain += gainStepAllocate;
raiser += 2;
findings.Add(new Finding()
{
Numbers = n,
Stars = s,
Probability = SpecialFunctions.Binomial(NUMBERS, n)
* SpecialFunctions.Binomial(MAXNUMBERS - NUMBERS, NUMBERS - n)
/ SpecialFunctions.Binomial(MAXNUMBERS, NUMBERS)
* SpecialFunctions.Binomial(STARS, s)
* SpecialFunctions.Binomial(MAXSTARS - STARS, STARS - s)
/ SpecialFunctions.Binomial(MAXSTARS, STARS),
Gain = gainStepAllocate
});
}
}
return(findings);
}
private static void CalcularCoeficienteBinomial()
{
Console.WriteLine("1. Calcular o Coeficiente Binomial entre os números n e p");
while (true)
{
Console.WriteLine("Informe o número n entre 1 a 200 ( 999 -> Sai )");
string numero1 = Console.ReadLine();
Console.WriteLine("Informe o número p entre 1 a 200 ( 999 -> Sai )");
string numero2 = Console.ReadLine();
int n;
int p;
if (Int32.TryParse(numero1, out n))
{
if (n == 999)
{
break;
}
if (Int32.TryParse(numero2, out p))
{
if (p == 999)
{
break;
}
Console.WriteLine($" C({n},{p}) = {SpecialFunctions.Binomial(n, p).ToString("N")}");
Console.WriteLine();
}
else
{
Console.WriteLine("Valor de p inválido...");
}
}
else
{
Console.WriteLine("Valor de n inválido...");
}
}
}
/// <summary>
/// Returns the Matrix representing the Casteljau Algorithm for solving Bernstein functions
/// </summary>
/// <param name="numPoints">Number of points in this bezier curve</param>
/// <returns>Returns a sparse matrix of the order numPoints X numPoints</returns>
private Matrix <double> GetCasteljauMatrix(int numPoints)
{
if (_matrixCache.ContainsKey(numPoints))
{
return(_matrixCache[numPoints]);
}
Matrix <double> m = new MathNet.Numerics.LinearAlgebra.Double.SparseMatrix(numPoints, numPoints);
int n = numPoints - 1;
for (int i = 0; i <= n; i++)
{
for (int k = 0; k <= n - i; k++)
{
// m_ij = -1^(i+k+n)*(n-1 choose k)*(n choose i)
m[i, k] = Math.Pow(-1, i + k + n) *
SpecialFunctions.Binomial(n - i, k) *
SpecialFunctions.Binomial(n, i);
}
}
_matrixCache[numPoints] = m;
return(m);
}
/// <summary>
/// Computes the probability mass (PMF) at k, i.e. P(X = k).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
/// <returns>the probability mass at location <paramref name="k"/>.</returns>
public double Probability(int k)
{
return(SpecialFunctions.Binomial(_success, k) * SpecialFunctions.Binomial(_population - _success, _draws - k) / SpecialFunctions.Binomial(_population, _draws));
}
public void ValidateProbability(int N, int m, int n, int x)
{
var d = new Hypergeometric(N, m, n);
Assert.AreEqual <double>(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(N - m, n - x) / SpecialFunctions.Binomial(N, n), d.Probability(x));
}
/// <summary>
/// Executes the example.
/// </summary>
public override void ExecuteExample()
{
// <seealso cref="http://en.wikipedia.org/wiki/Beta_function">Beta function</seealso>
MathDisplay.WriteLine("<b>Beta fuction</b>");
// 1. Compute the Beta function at z = 1.0, w = 3.0
MathDisplay.WriteLine(@"1. Compute the Beta function at z = 1.0, w = 3.0");
MathDisplay.WriteLine(SpecialFunctions.Beta(1.0, 3.0).ToString());
MathDisplay.WriteLine();
// 2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0
MathDisplay.WriteLine(@"2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0");
MathDisplay.WriteLine(SpecialFunctions.BetaLn(1.0, 3.0).ToString());
MathDisplay.WriteLine();
// 3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7
MathDisplay.WriteLine(@"3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7");
MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 0.7).ToString());
MathDisplay.WriteLine();
// 4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0
MathDisplay.WriteLine(@"4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0");
MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 1.0).ToString());
MathDisplay.WriteLine();
// 5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7
MathDisplay.WriteLine(@"5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7");
MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 0.7).ToString());
MathDisplay.WriteLine();
// 6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0
MathDisplay.WriteLine(@"6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0");
MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 1.0).ToString());
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Common functions</b>");
// 1. Calculate the Digamma function at point 5.0
// <seealso cref="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</seealso>
MathDisplay.WriteLine(@"1. Calculate the Digamma function at point 5.0");
MathDisplay.WriteLine(SpecialFunctions.DiGamma(5.0).ToString());
MathDisplay.WriteLine();
// 2. Calculate the inverse Digamma function at point 1.5
MathDisplay.WriteLine(@"2. Calculate the inverse Digamma function at point 1.5");
MathDisplay.WriteLine(SpecialFunctions.DiGammaInv(1.5).ToString());
MathDisplay.WriteLine();
// 3. Calculate the 10'th Harmonic number
// <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number">Harmonic number</seealso>
MathDisplay.WriteLine(@"3. Calculate the 10'th Harmonic number");
MathDisplay.WriteLine(SpecialFunctions.Harmonic(10).ToString());
MathDisplay.WriteLine();
// 4. Calculate the generalized harmonic number of order 10 of 3.0.
// <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers">Generalized harmonic numbers</seealso>
MathDisplay.WriteLine(@"4. Calculate the generalized harmonic number of order 10 of 3.0");
MathDisplay.WriteLine(SpecialFunctions.GeneralHarmonic(10, 3.0).ToString());
MathDisplay.WriteLine();
// 5. Calculate the logistic function of 3.0
// <seealso cref="http://en.wikipedia.org/wiki/Logistic_function">Logistic function</seealso>
MathDisplay.WriteLine(@"5. Calculate the logistic function of 3.0");
MathDisplay.WriteLine(SpecialFunctions.Logistic(3.0).ToString());
MathDisplay.WriteLine();
// 6. Calculate the logit function of 0.3
// <seealso cref="http://en.wikipedia.org/wiki/Logit">Logit function</seealso>
MathDisplay.WriteLine(@"6. Calculate the logit function of 0.3");
MathDisplay.WriteLine(SpecialFunctions.Logit(0.3).ToString());
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Error_function">Error function</seealso>
MathDisplay.WriteLine("<b>Error function</b>");
// 1. Calculate the error function at point 2
MathDisplay.WriteLine(@"1. Calculate the error function at point 2");
MathDisplay.WriteLine(SpecialFunctions.Erf(2).ToString());
MathDisplay.WriteLine();
// 2. Sample 10 values of the error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"2. Sample 10 values of the error function in [-1.0; 1.0]");
var data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erf);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Calculate the complementary error function at point 2
MathDisplay.WriteLine(@"3. Calculate the complementary error function at point 2");
MathDisplay.WriteLine(SpecialFunctions.Erfc(2).ToString());
MathDisplay.WriteLine();
// 4. Sample 10 values of the complementary error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"4. Sample 10 values of the complementary error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erfc);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 5. Calculate the inverse error function at point z=0.5
MathDisplay.WriteLine(@"5. Calculate the inverse error function at point z=0.5");
MathDisplay.WriteLine(SpecialFunctions.ErfInv(0.5).ToString());
MathDisplay.WriteLine();
// 6. Sample 10 values of the inverse error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"6. Sample 10 values of the inverse error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfInv);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 7. Calculate the complementary inverse error function at point z=0.5
MathDisplay.WriteLine(@"7. Calculate the complementary inverse error function at point z=0.5");
MathDisplay.WriteLine(SpecialFunctions.ErfcInv(0.5).ToString());
MathDisplay.WriteLine();
// 8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]
MathDisplay.WriteLine(@"8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]");
data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfcInv);
for (var i = 0; i < data.Length; i++)
{
MathDisplay.Write(data[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Factorial">Factorial</seealso>
MathDisplay.WriteLine("<b>Factorial</b>");
// 1. Compute the factorial of 5
MathDisplay.WriteLine(@"1. Compute the factorial of 5");
MathDisplay.WriteLine(SpecialFunctions.Factorial(5).ToString("N"));
MathDisplay.WriteLine();
// 2. Compute the logarithm of the factorial of 5
MathDisplay.WriteLine(@"2. Compute the logarithm of the factorial of 5");
MathDisplay.WriteLine(SpecialFunctions.FactorialLn(5).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Binomial_coefficient">Binomial coefficient</seealso>
MathDisplay.WriteLine("<b>Binomial coefficient</b>");
// 3. Compute the binomial coefficient: 10 choose 8
MathDisplay.WriteLine(@"3. Compute the binomial coefficient: 10 choose 8");
MathDisplay.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N"));
MathDisplay.WriteLine();
// 4. Compute the logarithm of the binomial coefficient: 10 choose 8
MathDisplay.WriteLine(@"4. Compute the logarithm of the binomial coefficient: 10 choose 8");
MathDisplay.WriteLine(SpecialFunctions.BinomialLn(10, 8).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</seealso>
MathDisplay.WriteLine("<b>Multinomial coefficient</b>");
// 5. Compute the multinomial coefficient: 10 choose 2, 3, 5
MathDisplay.WriteLine(@"5. Compute the multinomial coefficient: 10 choose 2, 3, 5");
MathDisplay.WriteLine(SpecialFunctions.Multinomial(10, new[] { 2, 3, 5 }).ToString("N"));
MathDisplay.WriteLine();
// <seealso cref="http://en.wikipedia.org/wiki/Gamma_function">Gamma function</seealso>
MathDisplay.WriteLine("<b>Gamma function</b>");
// 1. Compute the Gamma function of 10
MathDisplay.WriteLine(@"1. Compute the Gamma function of 10");
MathDisplay.WriteLine(SpecialFunctions.Gamma(10).ToString("N"));
MathDisplay.WriteLine();
// 2. Compute the logarithm of the Gamma function of 10
MathDisplay.WriteLine(@"2. Compute the logarithm of the Gamma function of 10");
MathDisplay.WriteLine(SpecialFunctions.GammaLn(10).ToString("N"));
MathDisplay.WriteLine();
// 3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14
MathDisplay.WriteLine(@"3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 14).ToString("N"));
MathDisplay.WriteLine();
// 4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100
MathDisplay.WriteLine(@"4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 100).ToString("N"));
MathDisplay.WriteLine();
// 5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0
MathDisplay.WriteLine(@"5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperIncomplete(10, 0).ToString("N"));
MathDisplay.WriteLine();
// 6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 10
MathDisplay.WriteLine(@"6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 10).ToString("N"));
MathDisplay.WriteLine();
// 7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14
MathDisplay.WriteLine(@"7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 14).ToString("N"));
MathDisplay.WriteLine();
// 8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100
MathDisplay.WriteLine(@"8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 100).ToString("N"));
MathDisplay.WriteLine();
// 9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0
MathDisplay.WriteLine(@"9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 0).ToString("N"));
MathDisplay.WriteLine();
// 10. Compute the upper regularized gamma(a, x) function at a = 10, x = 10
MathDisplay.WriteLine(@"10. Compute the upper regularized gamma(a, x) function at a = 10, x = 100");
MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 10).ToString("N"));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Numerical stability</b>");
// 1. Compute numerically stable exponential of 10 minus one
MathDisplay.WriteLine(@"1. Compute numerically stable exponential of 4.2876 minus one");
MathDisplay.WriteLine(SpecialFunctions.ExponentialMinusOne(4.2876).ToString());
MathDisplay.WriteLine();
// 2. Compute regular System.Math exponential of 15.28 minus one
MathDisplay.WriteLine(@"2. Compute regular System.Math exponential of 4.2876 minus one ");
MathDisplay.WriteLine((Math.Exp(4.2876) - 1).ToString());
MathDisplay.WriteLine();
// 3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3
MathDisplay.WriteLine(@"3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3");
MathDisplay.WriteLine(SpecialFunctions.Hypotenuse(5, 3).ToString());
MathDisplay.WriteLine();
}
public void ValidateProbability(int size, int m, int n, int x)
{
var d = new Hypergeometric(size, m, n);
Assert.AreEqual(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(size - m, n - x) / SpecialFunctions.Binomial(size, n), d.Probability(x));
}
/// <summary>
/// Computes values of the probability mass function.
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
/// <returns>
/// the probability mass at location <paramref name="k"/>.
/// </returns>
public double Probability(int k)
{
return(SpecialFunctions.Binomial(_m, k) * SpecialFunctions.Binomial(_populationSize - _m, _n - k) / SpecialFunctions.Binomial(_populationSize, _n));
}
public void ValidateProbability(int population, int success, int draws, int x)
{
var d = new Hypergeometric(population, success, draws);
Assert.AreEqual(SpecialFunctions.Binomial(success, x) * SpecialFunctions.Binomial(population - success, draws - x) / SpecialFunctions.Binomial(population, draws), d.Probability(x));
}