/// <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 cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
/// </summary>
/// <param name="x">The location at which to compute the cumulative distribution 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 cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CumulativeDistribution"/>
public static double CDF(int population, int success, int draws, double x)
{
if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
if (x < System.Math.Max(0, draws + success - population))
{
return(0.0);
}
if (x >= System.Math.Min(success, draws))
{
return(1.0);
}
var k = (int)System.Math.Floor(x);
var denominatorLn = SpecialFunctions.BinomialLn(population, draws);
var sum = 0.0;
for (var i = 0; i <= k; i++)
{
sum += System.Math.Exp(SpecialFunctions.BinomialLn(success, i) + SpecialFunctions.BinomialLn(population - success, draws - i) - denominatorLn);
}
return(sum);
}
/// <summary>
/// Computes values of the log probability mass function.
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
public double ProbabilityLn(int k)
{
if (k < 0)
{
return(Double.NegativeInfinity);
}
if (k > _n)
{
return(Double.NegativeInfinity);
}
if (_p == 0.0 && k == 0)
{
return(0.0);
}
if (_p == 0.0)
{
return(Double.NegativeInfinity);
}
if (_p == 1.0 && k == _n)
{
return(0.0);
}
if (_p == 1.0)
{
return(Double.NegativeInfinity);
}
return(SpecialFunctions.BinomialLn(_n, k) + (k * Math.Log(_p)) + ((_n - k) * Math.Log(1.0 - _p)));
}
/// <summary>
/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the log 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 log probability mass at location <paramref name="k"/>.</returns>
public static double PMFLn(int population, int success, int draws, int k)
{
if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
return(SpecialFunctions.BinomialLn(success, k) + SpecialFunctions.BinomialLn(population - success, draws - k) - SpecialFunctions.BinomialLn(population, draws));
}
/// <summary>
/// Ported from Fortran
/// Modifies pExcd
/// </summary>
/// <param name="nPerm"></param>
/// <param name="n1s"></param>
/// <param name="sbdry"></param>
/// <param name="sbdryOffset"></param>
/// <param name="pExcd"></param>
private static void PExceed(uint nPerm, uint n1s, uint[] sbdry, uint sbdryOffset,
out double pExcd)
{
double dlcnk;
int i, n, k, n1, k1, n2, k2, n3, k3;
n = Convert.ToInt32(nPerm);
k = Convert.ToInt32(n1s);
n1 = Convert.ToInt32(nPerm - sbdry[sbdryOffset]);
dlcnk = SpecialFunctions.BinomialLn(n, k);
pExcd = Math.Exp(
SpecialFunctions.BinomialLn(n1, k) - dlcnk);
if (n1s >= 2)
{
n1 = Convert.ToInt32(sbdry[sbdryOffset]);
n = Convert.ToInt32(nPerm - sbdry[sbdryOffset + 1]);
k = Convert.ToInt32(n1s - 1);
pExcd += Math.Exp(Math.Log(n1) + SpecialFunctions.BinomialLn(n, k) -
dlcnk);
}
if (n1s >= 3)
{
n1 = Convert.ToInt32(sbdry[sbdryOffset]);
n2 = Convert.ToInt32(sbdry[sbdryOffset + 1]);
n = Convert.ToInt32(nPerm - sbdry[sbdryOffset + 2]);
k = Convert.ToInt32(n1s - 2);
pExcd += Math.Exp(Math.Log(n1) + Math.Log(n1 - 1.0) - Math.Log(2.0) +
SpecialFunctions.BinomialLn(n, k) - dlcnk) +
Math.Exp(Math.Log(n1) + Math.Log(n2 - n1) +
SpecialFunctions.BinomialLn(n, k) - dlcnk);
}
if (n1s > 3)
{
for (i = 4; i <= n1s; i++)
{
n1 = Convert.ToInt32(sbdry[sbdryOffset + i - 4]);
k1 = i - 1;
k2 = i - 2;
k3 = i - 3;
n2 = Convert.ToInt32(sbdry[sbdryOffset + i - 3]);
n3 = Convert.ToInt32(sbdry[sbdryOffset + i - 2]);
n = Convert.ToInt32(nPerm - sbdry[sbdryOffset + i - 1]);
k = Convert.ToInt32(n1s - i + 1);
pExcd += Math.Exp(SpecialFunctions.BinomialLn(n1, k1) +
SpecialFunctions.BinomialLn(n, k) - dlcnk) +
Math.Exp(SpecialFunctions.BinomialLn(n1, k2) +
Math.Log(n3 - n1) +
SpecialFunctions.BinomialLn(n, k) - dlcnk) +
Math.Exp(SpecialFunctions.BinomialLn(n1, k3) +
Math.Log(n2 - n1) + Math.Log(n3 - n2) +
SpecialFunctions.BinomialLn(n, k) - dlcnk) +
Math.Exp(SpecialFunctions.BinomialLn(n1, k3) +
Math.Log(n2 - n1) - Math.Log(2.0) + Math.Log(n2 - n1 - 1.0) +
SpecialFunctions.BinomialLn(n, k) - dlcnk);
}
}
}
public void CanComputeBinomialLn()
{
AssertHelpers.AlmostEqualRelative(Math.Log(1), SpecialFunctions.BinomialLn(1, 1), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(10), SpecialFunctions.BinomialLn(5, 2), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(35), SpecialFunctions.BinomialLn(7, 3), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(1), SpecialFunctions.BinomialLn(1, 0), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(0), SpecialFunctions.BinomialLn(0, 1), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(0), SpecialFunctions.BinomialLn(5, 7), 14);
AssertHelpers.AlmostEqualRelative(Math.Log(0), SpecialFunctions.BinomialLn(5, -7), 14);
}
/// <summary>
/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
/// <param name="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
/// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
public static double PMFLn(double p, int n, int k)
{
if (!(p >= 0.0 && p <= 1.0 && n >= 0))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
if (k < 0 || k > n)
{
return(Double.NegativeInfinity);
}
if (p == 0.0)
{
return(k == 0 ? 0.0 : Double.NegativeInfinity);
}
if (p == 1.0)
{
return(k == n ? 0.0 : Double.NegativeInfinity);
}
return(SpecialFunctions.BinomialLn(n, k) + (k * Math.Log(p)) + ((n - k) * Math.Log(1.0 - p)));
}
/// <summary>
/// Computes the cumulative distribution function (CDF) of the distribution, i.e. P(X <= x).
/// </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)
{
if (x < Minimum)
{
return 0.0;
}
if (x >= Maximum)
{
return 1.0;
}
var k = (int) Math.Floor(x);
var denominatorLn = SpecialFunctions.BinomialLn(_population, _draws);
var sum = 0.0;
for (var i = 0; i <= k; i++)
{
sum += Math.Exp(SpecialFunctions.BinomialLn(_success, i) + SpecialFunctions.BinomialLn(_population - _success, _draws - i) - denominatorLn);
}
return sum;
}
/// <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="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
/// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
/// <returns>the probability mass at location <paramref name="k"/>.</returns>
public static double PMF(double p, int n, int k)
{
//if (!(p >= 0.0 && p <= 1.0 && n >= 0)) {
// throw new ArgumentException("InvalidDistributionParameters");
//}
if (k < 0 || k > n)
{
return(0.0);
}
if (p == 0.0)
{
return(k == 0 ? 1.0 : 0.0);
}
if (p == 1.0)
{
return(k == n ? 1.0 : 0.0);
}
return(Math.Exp(SpecialFunctions.BinomialLn(n, k) + (k * Math.Log(p)) + ((n - k) * Math.Log(1.0 - p))));
}
/// <summary>
/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
public double ProbabilityLn(int k)
{
return(SpecialFunctions.BinomialLn(_success, k) + SpecialFunctions.BinomialLn(_population - _success, _draws - k) - SpecialFunctions.BinomialLn(_population, _draws));
}
/// <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();
}