public override void ExecuteExample()
{
// <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution</a>
MathDisplay.WriteLine("<b>Binomial distribution</b>");
// 1. Initialize the new instance of the Binomial distribution class with parameters P = 0.2, N = 20
var binomial = new Binomial(0.2, 20);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Binomial distribution class with parameters P = {0}, N = {1}", binomial.P, binomial.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomial.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomial.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomial.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", binomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", binomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Binomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Binomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Bernoulli distribution</a>
MathDisplay.WriteLine("<b>Bernoulli distribution</b>");
// 1. Initialize the new instance of the Bernoulli distribution class with parameter P = 0.2
var bernoulli = new Bernoulli(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Bernoulli distribution class with parameter P = {0}", bernoulli.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", bernoulli);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", bernoulli.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", bernoulli.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", bernoulli.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", bernoulli.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", bernoulli.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", bernoulli.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", bernoulli.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", bernoulli.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", bernoulli.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", bernoulli.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", bernoulli.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Bernoulli distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Bernoulli distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(bernoulli.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Categorical_distribution">Categorical distribution</a>
MathDisplay.WriteLine("<b>Categorical distribution</b>");
// 1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)
var binomialC = new Categorical(new[] { 0.1, 0.2, 0.25, 0.45 });
MathDisplay.WriteLine(@"1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)");
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomialC);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomialC.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomialC.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomialC.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomialC.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomialC.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomialC.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomialC.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomialC.Median.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomialC.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomialC.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the Categorical distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Categorical distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomialC.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution">ConwayMaxwellPoisson distribution</a>
MathDisplay.WriteLine("<b>Conway Maxwell Poisson distribution</b>");
// 1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = 2, Nu = 1
var conwayMaxwellPoisson = new ConwayMaxwellPoisson(2, 1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = {0}, Nu = {1}", conwayMaxwellPoisson.Lambda, conwayMaxwellPoisson.Nu);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", conwayMaxwellPoisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", conwayMaxwellPoisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", conwayMaxwellPoisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", conwayMaxwellPoisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", conwayMaxwellPoisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", conwayMaxwellPoisson.Mean.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", conwayMaxwellPoisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", conwayMaxwellPoisson.StdDev.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the ConwayMaxwellPoisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the ConwayMaxwellPoisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(conwayMaxwellPoisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Discrete_uniform">DiscreteUniform distribution</a>
MathDisplay.WriteLine("<b>Discrete Uniform distribution</b>");
// 1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = 2, UpperBound = 10
var discreteUniform = new DiscreteUniform(2, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = {0}, UpperBound = {1}", discreteUniform.LowerBound, discreteUniform.UpperBound);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", discreteUniform);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", discreteUniform.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", discreteUniform.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", discreteUniform.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", discreteUniform.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", discreteUniform.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", discreteUniform.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", discreteUniform.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", discreteUniform.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", discreteUniform.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", discreteUniform.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", discreteUniform.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", discreteUniform.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the DiscreteUniform distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the DiscreteUniform distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(discreteUniform.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Geometric distribution</a>
MathDisplay.WriteLine("<b>Geometric distribution</b>");
// 1. Initialize the new instance of the Geometric distribution class with parameter P = 0.2
var geometric = new Geometric(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Geometric distribution class with parameter P = {0}", geometric.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", geometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", geometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", geometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", geometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", geometric.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", geometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", geometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", geometric.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", geometric.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", geometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", geometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", geometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", geometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Geometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Geometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(geometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution</a>
MathDisplay.WriteLine("<b>Hypergeometric distribution</b>");
// 1. Initialize the new instance of the Hypergeometric distribution class with parameters PopulationSize = 10, M = 2, N = 8
var hypergeometric = new Hypergeometric(30, 15, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Hypergeometric distribution class with parameters Population = {0}, Success = {1}, Draws = {2}", hypergeometric.Population, hypergeometric.Success, hypergeometric.Draws);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", hypergeometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", hypergeometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", hypergeometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", hypergeometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", hypergeometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", hypergeometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", hypergeometric.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", hypergeometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", hypergeometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", hypergeometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", hypergeometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Hypergeometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Hypergeometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(hypergeometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Negative_binomial">NegativeBinomial distribution</a>
MathDisplay.WriteLine("<b>Negative Binomial distribution</b>");
// 1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = 0.2, R = 20
var negativeBinomial = new NegativeBinomial(20, 0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = {0}, N = {1}", negativeBinomial.P, negativeBinomial.R);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", negativeBinomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", negativeBinomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", negativeBinomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", negativeBinomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", negativeBinomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", negativeBinomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", negativeBinomial.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", negativeBinomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", negativeBinomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", negativeBinomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", negativeBinomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the NegativeBinomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the NegativeBinomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(negativeBinomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>
MathDisplay.WriteLine("<b>Poisson distribution</b>");
// 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1
var poisson = new Poisson(1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", poisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Poisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Poisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(poisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Zipf_distribution">Zipf distribution</a>
MathDisplay.WriteLine("<b>Zipf distribution</b>");
// 1. Initialize the new instance of the Zipf distribution class with parameters S = 5, N = 10
var zipf = new Zipf(5, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Zipf distribution class with parameters S = {0}, N = {1}", zipf.S, zipf.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", zipf);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", zipf.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", zipf.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", zipf.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", zipf.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", zipf.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", zipf.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", zipf.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", zipf.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", zipf.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", zipf.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", zipf.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Zipf distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Zipf distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(zipf.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
}
/// <summary>
/// Examples of generic function sampling and quantization providers
/// </summary>
public override void ExecuteExample()
{
MathDisplay.WriteLine("<b>Chebyshev sampling</b>");
// 1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the first kind within interval [0, 10]
var roots = FindRoots.ChebychevPolynomialFirstKind(20, 0, 10);
var result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the first kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the second kind within interval [0, 10]
roots = FindRoots.ChebychevPolynomialSecondKind(20, 0, 10);
result = Generate.Map <double, double>(roots, Function);
MathDisplay.WriteLine(@"2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of
the second kind within interval [0, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Equidistant sampling</b>");
// 1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]
result = Generate.LinearSpacedMap <double>(11, -5, 5, Function);
MathDisplay.WriteLine(@"1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points
double[] samplePoints = Generate.LinearSpaced(10, 1.0, 5.5);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5
result = Generate.PeriodicMap <double>(10, Function, 10, 1.0, 10, 5);
MathDisplay.WriteLine(@"3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Random sampling</b>");
// 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]
var uniform = new ContinuousUniform(-10, 10);
result = Generate.RandomMap <double>(10, uniform, Function);
MathDisplay.WriteLine(@" 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform
distribution on [-10, 10]");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points
var exponential = new Exponential(1);
samplePoints = Generate.Random(10, exponential);
result = Generate.Map <double, double>(samplePoints, Function);
MathDisplay.WriteLine(@"2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution
and retrieve sample points");
MathDisplay.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
MathDisplay.Write(samplePoints[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution
var chiSquare = new ChiSquared(10);
result = Generate.RandomMap2 <double>(10, chiSquare, TwoDomainFunction);
MathDisplay.WriteLine(@" 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution");
for (var i = 0; i < result.Length; i++)
{
MathDisplay.Write(result[i].ToString("N") + @" ");
}
MathDisplay.WriteLine();
}
/// <summary>
/// Executes the example.
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Random_number_generation">Random number generation</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Linear_congruential_generator">Linear congruential generator</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Mersenne_twister">Mersenne twister</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Lagged_Fibonacci_generator">Lagged Fibonacci generator</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Xorshift">Xorshift</seealso>
public override void ExecuteExample()
{
// All RNG classes in MathNet have the following counstructors:
// - RNG(int seed, bool threadSafe): initializes a new instance using a specific seed value and thread
// safe property
// - RNG(int seed): initializes a new instance using a specific seed value. Thread safe property is set
// to Control.ThreadSafeRandomNumberGenerators
// - RNG(bool threadSafe) : initializes a new instance with the seed value set to DateTime.Now.Ticks and
// specific thread safe property
// - RNG(bool threadSafe) : initializes a new instance with the seed value set to DateTime.Now.Ticks and
// thread safe property set to Control.ThreadSafeRandomNumberGenerators
// All RNG classes in MathNet have next methods to produce random values:
// - double[] NextDouble(int n): returns an "n"-size array of uniformly distributed random doubles in
// the interval [0.0,1.0];
// - int Next(): returns a nonnegative random number;
// - int Next(int maxValue): returns a random number less then a specified maximum;
// - int Next(int minValue, int maxValue): returns a random number within a specified range;
// - void NextBytes(byte[] buffer): fills the elements of a specified array of bytes with random numbers;
// All RNG classes in MathNet have next extension methods to produce random values:
// - long NextInt64(): returns a nonnegative random number less than "Int64.MaxValue";
// - int NextFullRangeInt32(): returns a random number of the full Int32 range;
// - long NextFullRangeInt64(): returns a random number of the full Int64 range;
// - decimal NextDecimal(): returns a nonnegative decimal floating point random number less than 1.0;
// 1. Multiplicative congruential generator using a modulus of 2^31-1 and a multiplier of 1132489760
var mcg31M1 = new Mcg31m1(1);
MathDisplay.WriteLine(@"1. Generate 10 random double values using Multiplicative congruential generator with a
modulus of 2^31-1 and a multiplier of 1132489760");
var randomValues = mcg31M1.NextDoubles(10);
for (var i = 0; i < randomValues.Length; i++)
{
MathDisplay.Write(randomValues[i].ToString("N") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 2. Multiplicative congruential generator using a modulus of 2^59 and a multiplier of 13^13
var mcg59 = new Mcg59(1);
MathDisplay.WriteLine(@"2. Generate 10 random integer values using Multiplicative congruential generator with a
modulus of 2^59 and a multiplier of 13^13");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mcg59.Next() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 3. Random number generator using Mersenne Twister 19937 algorithm
var mersenneTwister = new MersenneTwister(1);
MathDisplay.WriteLine(@"3. Generate 10 random integer values less then 100 using Mersenne Twister 19937 algorithm");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mersenneTwister.Next(100) + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 4. Multiple recursive generator with 2 components of order 3
var mrg32K3A = new Mrg32k3a(1);
MathDisplay.WriteLine(@"4. Generate 10 random integer values in range [50;100] using multiple recursive generator
with 2 components of order 3");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(mrg32K3A.Next(50, 100) + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 5. Parallel Additive Lagged Fibonacci pseudo-random number generator
var palf = new Palf(1);
MathDisplay.WriteLine(@"5. Generate 10 random bytes using Parallel Additive Lagged Fibonacci pseudo-random number
generator");
var bytes = new byte[10];
palf.NextBytes(bytes);
for (var i = 0; i < bytes.Length; i++)
{
MathDisplay.Write(bytes[i] + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 6. A random number generator based on "System.Security.Cryptography.RandomNumberGenerator" class in
// the .NET library
var systemCrypto = new CryptoRandomSource();
MathDisplay.WriteLine(@"6. Generate 10 random decimal values using RNG based on
'System.Security.Cryptography.RandomNumberGenerator'");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(systemCrypto.NextDecimal().ToString("N") + @" ");
}
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 7. Wichmann-Hill’s 1982 combined multiplicative congruential generator
var rngWh1982 = new WH1982();
MathDisplay.WriteLine(@"7. Generate 10 random full Int32 range values using Wichmann-Hill’s 1982 combined
multiplicative congruential generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(rngWh1982.NextFullRangeInt32() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 8. Wichmann-Hill’s 2006 combined multiplicative congruential generator.
var rngWh2006 = new WH2006();
MathDisplay.WriteLine(@"8. Generate 10 random full Int64 range values using Wichmann-Hill’s 2006 combined
multiplicative congruential generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(rngWh2006.NextFullRangeInt32() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// 9. Multiply-with-carry Xorshift pseudo random number generator
var xorshift = new Xorshift();
MathDisplay.WriteLine(@"9. Generate 10 random nonnegative values less than Int64.MaxValue using
Multiply-with-carry Xorshift pseudo random number generator");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(xorshift.NextInt64() + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
}
/// <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();
}
