/// <summary>
/// Run example
/// </summary>
public void Run()
{
// 1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]
var result = SignalGenerator.EquidistantInterval(Function, -5, 5, 11);
Console.WriteLine(@"1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.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;
result = SignalGenerator.EquidistantStartingAt(Function, 1, 0.5, 10, out samplePoints);
Console.WriteLine(@"2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points");
Console.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
Console.Write(samplePoints[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5
result = SignalGenerator.EquidistantPeriodic(Function, 10, 5, 10);
Console.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++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Sample f(x) = (x * x) / 2 equidistant to an integer-domain function starting at x = 0 and step = 2
var equidistant = SignalGenerator.EquidistantToFunction(Function, 0, 2);
Console.WriteLine(@" 4. Sample f(x) = (x * x) / 2 equidistant to an integer-domain function starting at x = 0 and step = 2");
for (var i = 0; i < 10; i++)
{
Console.Write(equidistant(i).ToString("N") + @" ");
}
Console.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Spline_interpolation">Spline interpolation</seealso>
public void Run()
{
// 1. Generate 10 samples of the function x*x-2*x on interval [0, 10]
Console.WriteLine(@"1. Generate 10 samples of the function x*x-2*x on interval [0, 10]");
double[] points;
var values = SignalGenerator.EquidistantInterval(TargetFunction, 0, 10, 10, out points);
Console.WriteLine();
// 2. Create akima spline interpolation
var method = new AkimaSplineInterpolation(points, values);
Console.WriteLine(@"2. Create akima spline interpolation based on arbitrary points");
Console.WriteLine();
// 3. Check if interpolation support integration
Console.WriteLine(@"3. Support integration = {0}", ((IInterpolation)method).SupportsIntegration);
Console.WriteLine();
// 4. Check if interpolation support differentiation
Console.WriteLine(@"4. Support differentiation = {0}", ((IInterpolation)method).SupportsDifferentiation);
Console.WriteLine();
// 5. Differentiate at point 5.2
Console.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
Console.WriteLine();
// 6. Integrate at point 5.2
Console.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
Console.WriteLine();
// 7. Interpolate ten random points and compare to function results
Console.WriteLine(@"7. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 10]
var point = rng.NextDouble() * 10;
Console.WriteLine(@"Interpolate at {0} = {1}. Function({0}) = {2}", point.ToString("N05"), method.Interpolate(point).ToString("N05"), TargetFunction(point).ToString("N05"));
}
Console.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Interpolation">Interpolation</seealso>
public void Run()
{
// 1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]
Console.WriteLine(@"1. Generate 10 samples of the function 1/(1+x*x) on interval [-5, 5]");
double[] points;
var values = SignalGenerator.EquidistantInterval(TargetFunction, -5, 5, 10, out points);
Console.WriteLine();
// 2. Create a floater hormann rational pole-free interpolation based on arbitrary points
// This method is used by default when create an interpolation using Interpolate.Common method
var method = Interpolate.RationalWithoutPoles(points, values);
Console.WriteLine(@"2. Create a floater hormann rational pole-free interpolation based on arbitrary points");
Console.WriteLine();
// 3. Check if interpolation support integration
Console.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
Console.WriteLine();
// 4. Check if interpolation support differentiation
Console.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
Console.WriteLine();
// 5. Interpolate ten random points and compare to function results
Console.WriteLine(@"5. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.NextDouble() * 5;
Console.WriteLine(@"Interpolate at {0} = {1}. Function({0}) = {2}", point.ToString("N05"), method.Interpolate(point).ToString("N05"), TargetFunction(point).ToString("N05"));
}
Console.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// 1. Generate 20 samples of the function f(x) = x on interval [-5, 5]
Console.WriteLine(@"1. Generate 20 samples of the function f(x) = x on interval [-5, 5]");
double[] points;
var values = SignalGenerator.EquidistantInterval(TargetFunction, -5, 5, 20, out points);
Console.WriteLine();
// 2. Create a burlish stoer rational interpolation based on arbitrary points
var method = Interpolate.RationalWithPoles(points, values);
Console.WriteLine(@"2. Create a burlish stoer rational interpolation based on arbitrary points");
Console.WriteLine();
// 3. Check if interpolation support integration
Console.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
Console.WriteLine();
// 4. Check if interpolation support differentiation
Console.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
Console.WriteLine();
// 5. Interpolate ten random points and compare to function results
Console.WriteLine(@"5. Interpolate ten random points and compare to function results");
var rng = new MersenneTwister(1);
for (var i = 0; i < 10; i++)
{
// Generate random value from [0, 5]
var point = rng.Next(0, 5);
Console.WriteLine(@"Interpolate at {0} = {1}. Function({0}) = {2}", point.ToString("N05"), method.Interpolate(point).ToString("N05"), TargetFunction(point).ToString("N05"));
}
Console.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient">Pearson product-moment correlation coefficient</seealso>
public void Run()
{
// 1. Initialize the new instance of the ChiSquare distribution class with parameter dof = 5.
var chiSquare = new ChiSquared(5);
Console.WriteLine(@"1. Initialize the new instance of the ChiSquare distribution class with parameter DegreesOfFreedom = {0}", chiSquare.DegreesOfFreedom);
Console.WriteLine(@"{0} distributuion properties:", chiSquare);
Console.WriteLine(@"{0} - Largest element", chiSquare.Maximum.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Smallest element", chiSquare.Minimum.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Mean", chiSquare.Mean.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Median", chiSquare.Median.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Mode", chiSquare.Mode.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Variance", chiSquare.Variance.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 2. Generate 1000 samples of the ChiSquare(5) distribution
Console.WriteLine(@"2. Generate 1000 samples of the ChiSquare(5) distribution");
var data = new double[1000];
for (var i = 0; i < data.Length; i++)
{
data[i] = chiSquare.Sample();
}
// 3. Get basic statistics on set of generated data using extention methods
Console.WriteLine(@"3. Get basic statistics on set of generated data using extention methods");
Console.WriteLine(@"{0} - Largest element", data.Maximum().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Smallest element", data.Minimum().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Mean", data.Mean().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Median", data.Median().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Biased population variance", data.PopulationVariance().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Variance", data.Variance().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Standard deviation", data.StandardDeviation().ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Biased sample standard deviation", data.PopulationStandardDeviation().ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 4. Compute the basic statistics of data set using DescriptiveStatistics class
Console.WriteLine(@"4. Compute the basic statistics of data set using DescriptiveStatistics class");
var descriptiveStatistics = new DescriptiveStatistics(data);
Console.WriteLine(@"{0} - Kurtosis", descriptiveStatistics.Kurtosis.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Largest element", descriptiveStatistics.Maximum.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Smallest element", descriptiveStatistics.Minimum.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Mean", descriptiveStatistics.Mean.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Variance", descriptiveStatistics.Variance.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Standard deviation", descriptiveStatistics.StandardDeviation.ToString(" #0.00000;-#0.00000"));
Console.WriteLine(@"{0} - Skewness", descriptiveStatistics.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// Generate 1000 samples of the ChiSquare(2.5) distribution
var chiSquareB = new ChiSquared(2);
var dataB = new double[1000];
for (var i = 0; i < data.Length; i++)
{
dataB[i] = chiSquareB.Sample();
}
// 5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5)
Console.WriteLine(@"5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
Console.WriteLine(@"6. Ranked correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
Console.WriteLine();
// 6. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x
data = SignalGenerator.EquidistantInterval(x => x * 2, 0, 100, 1000);
dataB = SignalGenerator.EquidistantInterval(x => x * x, 0, 100, 1000);
Console.WriteLine(@"7. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
Console.WriteLine(@"8. Ranked correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
Console.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Error_function">Error function</seealso>
public void Run()
{
// 1. Calculate the error function at point 2
Console.WriteLine(@"1. Calculate the error function at point 2");
Console.WriteLine(SpecialFunctions.Erf(2));
Console.WriteLine();
// 2. Sample 10 values of the error function in [-1.0; 1.0]
Console.WriteLine(@"2. Sample 10 values of the error function in [-1.0; 1.0]");
var data = SignalGenerator.EquidistantInterval(SpecialFunctions.Erf, -1.0, 1.0, 10);
for (var i = 0; i < data.Length; i++)
{
Console.Write(data[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 3. Calculate the complementary error function at point 2
Console.WriteLine(@"3. Calculate the complementary error function at point 2");
Console.WriteLine(SpecialFunctions.Erfc(2));
Console.WriteLine();
// 4. Sample 10 values of the complementary error function in [-1.0; 1.0]
Console.WriteLine(@"4. Sample 10 values of the complementary error function in [-1.0; 1.0]");
data = SignalGenerator.EquidistantInterval(SpecialFunctions.Erfc, -1.0, 1.0, 10);
for (var i = 0; i < data.Length; i++)
{
Console.Write(data[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 5. Calculate the inverse error function at point z=0.5
Console.WriteLine(@"5. Calculate the inverse error function at point z=0.5");
Console.WriteLine(SpecialFunctions.ErfInv(0.5));
Console.WriteLine();
// 6. Sample 10 values of the inverse error function in [-1.0; 1.0]
Console.WriteLine(@"6. Sample 10 values of the inverse error function in [-1.0; 1.0]");
data = SignalGenerator.EquidistantInterval(SpecialFunctions.ErfInv, -1.0, 1.0, 10);
for (var i = 0; i < data.Length; i++)
{
Console.Write(data[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 7. Calculate the complementary inverse error function at point z=0.5
Console.WriteLine(@"7. Calculate the complementary inverse error function at point z=0.5");
Console.WriteLine(SpecialFunctions.ErfcInv(0.5));
Console.WriteLine();
// 8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]
Console.WriteLine(@"8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]");
data = SignalGenerator.EquidistantInterval(SpecialFunctions.ErfcInv, -1.0, 1.0, 10);
for (var i = 0; i < data.Length; i++)
{
Console.Write(data[i].ToString("N") + @" ");
}
Console.WriteLine();
}