/// <summary>
/// Run example
/// </summary>
public void Run()
{
// 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(roots, Function);
Console.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++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.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(roots, Function);
Console.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++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.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();
}
