VB.NET Polynomial Least Squares Example

Imports System

Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Analysis

Namespace CenterSpace.NMath.Analysis.Examples.VisualBasic

  ' A .NET example in VB.NET showing how to fit a polynomial through a set of points.
  Module PolynomialLeastSquaresExample

    Sub Main()

      Console.WriteLine()

      ' The points: (0.3, -0.9), (0.6, -0.6), (1.8, -13.4), (34.3, -19.3)
      Dim X As New DoubleVector(0.3, 0.6, 1.8, 34.3)
      Dim Y As New DoubleVector(-0.9, -0.6, -13.4, -19.3)

      ' Fit the best 2nd degree polynomial to the points.
      Dim lsq As New PolynomialLeastSquares(2, X, Y)
      Console.WriteLine("Best polynomial of degree " & lsq.Degree & " is: ")
      Console.WriteLine()
      Console.WriteLine(lsq.FittedPolynomial)
      Console.WriteLine()
      Console.WriteLine("residual sum of squares: " & lsq.LeastSquaresSolution.ResidualSumOfSquares)
      Console.WriteLine()
      Console.WriteLine()

      ' Fit the best 3rd degree polynomial to the points.
      lsq = New PolynomialLeastSquares(3, X, Y)
      Console.WriteLine("Best polynomial of degree " & lsq.Degree & " is: ")
      Console.WriteLine()
      Console.WriteLine(lsq.FittedPolynomial)
      Console.WriteLine()
      Console.WriteLine("residual sum of squares: " & lsq.LeastSquaresSolution.ResidualSumOfSquares)
      Console.WriteLine()
      Console.WriteLine()

      ' Fit the best 4th degree polynomial to the points.
      lsq = New PolynomialLeastSquares(4, X, Y)
      Console.WriteLine("Best polynomial of degree " & lsq.Degree & " is: ")
      Console.WriteLine()
      Console.WriteLine(lsq.FittedPolynomial)
      Console.WriteLine()
      Console.WriteLine("residual sum of squares: " & lsq.LeastSquaresSolution.ResidualSumOfSquares)
      Console.WriteLine()

      ' Evaluate the polynomial
      Dim P As Polynomial = lsq.FittedPolynomial
      Console.WriteLine("Polynomial evaluated at 4.5: " & P.Evaluate(4.5))
      Console.WriteLine()

      ' First derivative
      Console.WriteLine("Derivative of the polynomial: ")
      Console.WriteLine(P.Derivative())

      ' Second derivative
      Console.WriteLine("Second Derivative of the polynomial: ")
      Console.WriteLine(P.Derivative().Derivative())
      Console.WriteLine()

      ' Integrate
      Console.WriteLine("Integral of the polynomial from 3.2 to 4.6:")
      Console.WriteLine(P.Integrate(3.2, 4.6))

      Console.WriteLine()
      Console.WriteLine("Press Enter Key")
      Console.Read()

    End Sub

  End Module

End Namespace