VB Band Matrix Example

Imports System

Imports CenterSpace.NMath.Core


Namespace CenterSpace.NMath.Examples.VisualBasic

  A .NET example in Visual Basic exhibiting the features of the banded matrix classes.
  Module BandMatrixExample

    Sub Main()

      Set up the parameters that describe the shape of a banded matrix.
      Dim UpperBandwidth As Integer = 2
      Dim LowerBandwidth As Integer = 1
      Dim Rows As Integer = 7
      Dim Cols As Integer = 7

      Set up a banded matrix B by setting all the diagonals within the matrix 
      bandwidth.
      Dim B As New DoubleBandMatrix(Rows, Cols, LowerBandwidth, UpperBandwidth)
      Dim I As Integer
      For I = -B.LowerBandwidth To B.UpperBandwidth
        B.Diagonal(I).Set(Slice.All, I + 2)
      Next

      Console.WriteLine()
      Console.Write("B = ")
      Console.WriteLine(B.ToTabDelimited())

      B =
      2       3       4       0       0       0       0
      1       2       3       4       0       0       0
      0       1       2       3       4       0       0
      0       0       1       2       3       4       0
      0       0       0       1       2       3       4
      0       0       0       0       1       2       3
      0       0       0       0       0       1       2

      Indexer accessor works just like it does for general matrices. 
      Console.Write("B[2,2] = ")
      Console.WriteLine(B(2, 2))
      Console.Write("B[5,0] = ")
      Console.WriteLine(B(5, 0))

      You can set the values of elements in the bandwidth
      of a banded matrix using the indexer.
      B(2, 1) = 99
      Console.Write("B[2,1] = ")
      Console.WriteLine(B(2, 1))

      But setting an element outside the bandwidth of the
      matrix raises a NonModifiableElementException exception.
      Try
        B(6, 0) = 21
      Catch E As NonModifiableElementException
        Console.WriteLine()
        Console.Write("NonModifiableElementException: ")
        Console.WriteLine(E.Message)
      End Try

      Scalar multiplication and addition/subtraction is supported.
      Dim C As DoubleBandMatrix = 3 * B
      Dim D As DoubleBandMatrix = C - B
      Console.WriteLine()
      Console.WriteLine(D.ToTabDelimited())

      D =
      4       6       8       0       0       0       0
      2       4       6       8       0       0       0
      0       198     4       6       8       0       0
      0       0       2       4       6       8       0
      0       0       0       2       4       6       8
      0       0       0       0       2       4       6
      0       0       0       0       0       2       4

      Matrix/vector and matrix/matrix products too.
      Dim Rng As New RandGenUniform(-1, 1)
      Rng.Reset(&H124)
      Dim X As DoubleVector = New DoubleVector(B.Cols, Rng)  vector of random deviates

      Dim Y As DoubleVector = MatrixFunctions.Product(B, X)
      Console.Write("Bx = " & Y.ToString("G5"))

      Dim BTB As DoubleBandMatrix = MatrixFunctions.Product(B.Transpose(), B)
      Console.WriteLine()
      Console.WriteLine("BTB = ")
      Console.WriteLine(BTB.ToTabDelimited("G5"))

      You can transform the non-zero elements of a banded matrix object by using
      the Transform() method on its data vector.
      Dim CPi As DoubleBandMatrix = Math.PI * C
      CPi.DataVector.Transform(NMathFunctions.CosFunc)   cosine of Cpi
      Console.WriteLine("cos(Cpi) =")
      Console.WriteLine(CPi.ToTabDelimited("G5"))

      Since the inner product of two banded matrices is a banded matrix,
      matrix inner products is supported.
      Dim P As DoubleBandMatrix = MatrixFunctions.Product(CPi, C)
      Console.WriteLine("Banded matrix product =")
      Console.WriteLine(P.ToTabDelimited("G5"))

      You can also solve linear systems.
      Dim X2 As DoubleVector = MatrixFunctions.Solve(B, 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.WriteLine("||x - x2|| = " & ResidualL2Norm)

      You can use the Resize() method to change the bandwidths...
      CPi.Resize(CPi.Rows, CPi.Cols, 1, 1)   matrix is now tridiagonal.

      And construct a tridiagonal matrix from it.
      Dim T As DoubleTriDiagMatrix = New DoubleTriDiagMatrix(CPi)

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

    End Sub
  End Module
End Namespace