/// <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(); }