VB Integration Example

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Imports System

Imports CenterSpace.NMath.Core

Namespace CenterSpace.NMath.Core.Examples.VisualBasic

  ' A .NET example in Visual Basic showing how to create integrator objects for greater control
  ' over how numerical integration is performed.
  Module IntegrationExample

    Private Function MyFunction(ByVal X As Double) As Double
      Return Math.Sqrt(X)
    End Function

    Sub Main()


      Console.WriteLine("Known exact integral of f from 1 to 4 = 4.6666666...")

      ' As shown in the OneVariableFunctionExample, the Integrate() method
      ' on OneVariableFunction computes the integral of a function over a
      ' given interval.
      Dim D As Func(Of Double, Double) = AddressOf MyFunction
      Dim F As New OneVariableFunction(D)
      Console.Write("Estimate using default Romberg integrator = ")
      Console.WriteLine(F.Integrate(1, 4))

      ' To perform integration, every OneVariableFunction has an IIntegrator
      ' object associated with it. NMath Core integration classes such as
      ' RombergIntegrator and GaussKronrodIntegrator implement the IIntegrator
      ' interface. The default integrator for a OneVariableFunction is an instance
      ' of RombergIntegrator.

      ' Instances of class RombergIntegrator compute successive Romberg
      ' approximations of increasing order until the estimated error in the
      ' approximation is less than a specified error tolerance, or until the
      ' maximum order is reached. To achieve greater control over how integration
      ' is performed, you can instantiate your own RombergIntegrator.
      Dim Romberg As New RombergIntegrator()

      ' The Tolerance property gets and sets the error tolerance used in computing
      ' integrals. MaximumOrder gets and sets the maximum order.
      Romberg.Tolerance = 0.0000000001
      Romberg.MaximumOrder = 20

      ' The Integrate() method on RombergIntegrator accepts a
      ' OneVariableFunction and an interval over which to integrate.
      Console.Write("Estimate using customized Romberg integrator = ")
      Console.WriteLine(Romberg.Integrate(F, 1, 4))

      ' After computing an estimate, a RombergIntegrator holds a record of
      ' the iteration process. Read-only properties are provided for accessing
      ' this information.
      Console.Write("Order of estimate = ")
      Console.Write("Error estimate = ")

      ' ToleranceMet gets a boolean value indicating whether or not the error
      ' estimate for the integral approximation is less than the tolerance.
      if ( romberg.ToleranceMet ) 
        Console.WriteLine("The estimate is within the error tolerance.")
        Console.WriteLine("The estimate is NOT within the error tolerance.")
      End If

      ' Tableau gets the entire matrix of successive approximations
      ' computed while computing a Romberg estimate. The rows are the order
      ' of approximation. The columns are the level of approximation.
      ' The first column contains the trapezoidal approximations,
      ' the second column the Simpson’s rule approximations, the third
      ' column the Boole’s rule approximations, and so on, up to the Order
      ' of the approximation just computed.
      Console.WriteLine("Romberg Tableau...")

      ' The automatic GaussKronrodIntegrator class uses Gauss-Kronrod rules with
      ' increasing number of points. Approximation ends when the estimated error
      ' is less than a specified error tolerance, or when the maximum number of
      ' points is reached. The Gauss-Kronrod method is especially suited for
      ' non-singular oscillating integrands.
      Dim GK As New GaussKronrodIntegrator()
      Console.Write("Estimate using Gauss-Kronrod automatic integrator = ")
      Console.WriteLine(GK.Integrate(F, 1, 4))

      ' NMath Core also includes Gauss-Kronrod classes for different numbers of
      ' Kronrod points (2n+1, beginning with a Gauss 10-point rule). For instance,
      ' GaussKronrod21Integrator approximates integrals using the Gauss 10-point
      ' and the Kronrod 21-point rule.
      Dim GK21 As New GaussKronrod21Integrator()
      Console.Write("Estimate using Gauss-Kronrod 21 integrator = ")
      Console.WriteLine(GK21.Integrate(F, 1, 4))

      Console.WriteLine("Press Enter Key")

    End Sub
  End Module
End Namespace

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