VB.NET LU Factorization Example

Imports System

Imports CenterSpace.NMath.Core
Imports Range = CenterSpace.NMath.Core.Range

Namespace CenterSpace.NMath.Core.Examples.VisualBasic

  ' A .NET example in VB.NET showing how to use the LU factorization class to solve linear systems,
  ' and to compute matrix inverses, condition numbers and determinants.
  Module LUFactorizationExampple

    Sub Main()

      Console.WriteLine()

      Dim A As New DoubleMatrix("3x3 [2 1 1  4 1 0 -2 2 1]")
      Dim lu As New DoubleLUFact(A)
      ' Check to see if the input matrix is singular.
      If (lu.IsSingular) Then
        Console.WriteLine("Sorry, A is singular.")
        Return
      End If

      ' A is not singular, so we can look at the LU components.
      Console.WriteLine("L...")
      Console.WriteLine(lu.L.ToTabDelimited())

      Console.WriteLine("U...")
      Console.WriteLine(lu.U.ToTabDelimited())

      ' And the permutation matrix P.
      Console.WriteLine("P...")
      Console.WriteLine(lu.P.ToTabDelimited())

      ' We can also compute the determinant and condition number.
      Console.WriteLine("Determinant of A = {0}", lu.Determinant())

      ' We can choose to estimate the condition number (quick), or
      ' compute it directly (accurate). For small matrices these
      ' are usually the same.
      Dim estCond As Double = lu.ConditionNumber(NormType.InfinityNorm, True)
      Dim computedCond As Double = lu.ConditionNumber(NormType.OneNorm, False)
      Console.WriteLine("Estimated condition number, infinity-norm = {0}", estCond)
      Console.WriteLine("Computed condition number, 1-norm = {0}", computedCond)

      ' Finally, we can compute the inverse of A.
      Console.WriteLine("A inverse =")
      Console.WriteLine(lu.Inverse().ToTabDelimited())
      Console.WriteLine()

      ' We can use the LU factorization to solve for one right-hand side.
      Dim v As New DoubleVector("[8 11 3]")
      Dim u As DoubleVector = lu.Solve(v)
      Console.WriteLine("The solution, u, Au=v is...")
      Console.WriteLine(u)
      Console.WriteLine()

      ' Or we can solve for multiple right hand sides.
      Dim B As New DoubleMatrix(3, 3)

      ' Set all the columns of B to be the vector v.
      Dim i As Integer
      For i = 0 To 2
        B.Col(i)(Range.All) = v
      Next

      ' Now solve for AX=B. The columns of A should have the same values as
      ' the vector u from above.
      Dim X As DoubleMatrix = lu.Solve(B)
      Console.WriteLine("The solution, X, to AX=B is...")
      Console.WriteLine(X.ToTabDelimited())

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

    End Sub

  End Module

End Namespace