VB Triangular Matrix Example

Imports System

Imports CenterSpace.NMath.Core


Namespace CenterSpace.NMath.Examples.VisualBasic

  A .NET example in Visual Basic demonstrating the features of the triangular matrix classes.
  Module TriangularMatrixExample

    Sub Main()

      Set up the parameters that describe the shape of a Hermitian banded matrix.
      Dim Order As Integer = 5

      Create upper and lower triangular matrices.
      Dim Rng As New RandGenUniform(-1, 1)
      Rng.Reset(&H124)
      Dim A As New DoubleMatrix(Order, Order, Rng)
      Dim LU As New DoubleLUFact(A)
      Dim U As New DoubleUpperTriMatrix(LU.U)
      Dim L As New DoubleLowerTriMatrix(LU.L)

      Console.WriteLine()

      Console.WriteLine("U =")
      Console.WriteLine(U.ToTabDelimited("G3"))

      Console.WriteLine("L =")
      Console.WriteLine(L.ToTabDelimited("G3"))

      U =
      0.576   -0.325  -0.077  0.773   0.622
      0       -0.169  -0.142  0.0948  -0.916
      0       0       0.576   0.353   0.207
      0       0       0       -1.43   -1.01
      0       0       0       0       -0.581

      L =
      1       0       0       0       0
      0.34    1       0       0       0
      -0.863  0.581   1       0       0
      0.575   -0.843  0.401   1       0
      -0.434  0.398   0.422   -0.538  1

      Indexer accessor works just like it does for general matrices. 
      Console.WriteLine("U[2,2] = " & U(2, 2))
      Console.WriteLine("L[0,3] = " & L(0, 3))

      You can set the values of elements in the upper triangular part
      of a upper triangular matrix and the lower part of a lower
      triangular matrix.
      Dim Scalar As Double = 99
      L(2, 1) = Scalar
      Console.WriteLine("L[2,1] = " & L(2, 1)) 99
      U(0, 2) = Scalar + 1
      Console.WriteLine("U[0,2] = " & U(0, 2)) 100

      But setting the values of elements in the lower triangular part
      of a upper triangular matrix or the upper part of a lower
      triangular matrix raises a NonModifiableElementException.
      Try
        U(3, 0) = Scalar
      Catch E As NonModifiableElementException
        Console.WriteLine()
        Console.WriteLine("NonModifiableElementException: " & E.Message)
      End Try

      Try
        L(0, 3) = Scalar
      Catch E As NonModifiableElementException
        Console.WriteLine()
        Console.WriteLine("NonModifiableElementException: " & E.Message)
      End Try

      Scalar multiplication and matrix addition/subtraction are supported.
      Dim C As DoubleUpperTriMatrix = Scalar * U
      Dim D As DoubleUpperTriMatrix = C + U

      Console.WriteLine()
      Console.WriteLine("D =")
      Console.WriteLine(D.ToTabDelimited("G3"))

      Matrix/vector inner products too.
      Dim X As New DoubleVector(L.Cols, Rng)
      Dim Y As DoubleVector = MatrixFunctions.Product(L, X)

      Console.WriteLine("Lx = {0}", Y.ToString())

      You can transform the non-zero elements of a triangular matrix object
      by using the Transform() method on its data vector.
      Change every element of C to its absolute value.
      C.DataVector.Transform(NMathFunctions.AbsFunc)

      Console.WriteLine()
      Console.WriteLine("abs(C) =")
      Console.WriteLine(C.ToTabDelimited("G3"))

      You can also solve linear systems.
      Dim X2 As DoubleVector = MatrixFunctions.Solve(L, Y)

      x and x2 should be the same. Lets look at the l2 norm of
      their difference.
      Dim Residual As DoubleVector = X - X2
      Dim ResidualL2Norm As Double = Math.Sqrt(NMathFunctions.Dot(Residual, Residual))

      Console.Write("||x - x2|| = ")
      Console.WriteLine(ResidualL2Norm)

      You can calculate the determinant too.
      Dim Det As Double = MatrixFunctions.Determinant(U)

      Console.WriteLine()
      Console.Write("Determinant of U = ")
      Console.WriteLine(Det)

      You can use the Resize() method to change the bandwidths.
      D.Resize(6)

      Console.WriteLine()
      Console.WriteLine("D resized =")
      Console.WriteLine(D.ToTabDelimited("G3"))

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

    End Sub
  End Module
End Namespace