# VB Band Fact Example

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```Imports System

Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Matrix

Namespace CenterSpace.NMath.Matrix.Examples.VisualBasic

' A .NET example in Visual Basic demonstrating the features of the factorization classes for
' banded matrices.
Module BandFactExample

Sub Main()

' Construct a banded matrix with random entries from a data vector
' of the appropriate length.
Dim UpperBandwidth As Integer = 2
Dim LowerBandwidth As Integer = 1
Dim Rows As Integer = 7
Dim Cols As Integer = 7
Dim Rng As New RandGenUniform(-1, 1)
Rng.Reset(&H124)
Dim Data As New FloatVector((LowerBandwidth + UpperBandwidth + 1) * Cols, Rng)
Dim A As New FloatBandMatrix(Data, Rows, Cols, LowerBandwidth, UpperBandwidth)

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

' A =
' -0.25   0.182   -0.325  0       0       0       0
' 0.576   -0.0443 -0.28   0.22    0       0       0
' 0       0.0738  0.56    -0.077  -0.924  0       0
' 0       0       0.306   -0.168  0.621   -0.863  0
' 0       0       0       -0.259  0.773   0.203   -0.705
' 0       0       0       0       0.358   -0.585  0.124
' 0       0       0       0       0       0.622   0.87

' Construct a band factorization class.
Dim Fact As New FloatBandFact(A)

' Check to see if A is singular.
Dim IsSingularString As String
If Fact.IsSingular Then
IsSingularString = "A is singular"
Else
IsSingularString = "A is NOT singular"
End If
Console.WriteLine(IsSingularString)

' Retrieve information about the matrix A.
Dim Det As Single = Fact.Determinant()

' In order to get condition number, factor with estimateCondition = True
Fact.Factor(A, True)

Dim RCond As Single = Fact.ConditionNumber()
Dim AInv As FloatMatrix = Fact.Inverse()

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

Console.WriteLine()
Console.Write("Reciprocal condition number = ")
Console.WriteLine(RCond)

Console.WriteLine()
Console.WriteLine("A inverse =")
Console.WriteLine(AInv.ToTabDelimited("G5"))

' Use the factorization to solve some linear systems Ax = y.
Dim Y0 As New FloatVector(Fact.Cols, Rng)
Dim Y1 As New FloatVector(Fact.Cols, Rng)
Dim X0 As FloatVector = Fact.Solve(Y0)
Dim X1 As FloatVector = Fact.Solve(Y1)

Console.Write("Solution to Ax = y0 is ")
Console.WriteLine(X0.ToString())
Console.WriteLine()

Console.Write("y0 - Ax0 = ")
Console.WriteLine(FloatVector.Subtract(Y0, MatrixFunctions.Product(A, X0)).ToString("G3"))
Console.WriteLine()

Console.Write("Solution to Ax = y1 is")
Console.WriteLine(X1.ToString())
Console.WriteLine()

Console.Write("y1 - Ax1 = ")
Console.WriteLine(FloatVector.Subtract(Y1, MatrixFunctions.Product(A, X1)).ToString("G3"))

' You can also solve for multiple right-hand sides.
Dim Y As New FloatMatrix(Y1.Length, 2)
Y.Col(0)(Slice.All) = Y0
Y.Col(1)(Slice.All) = Y1
Dim X As FloatMatrix = Fact.Solve(Y)

' The first column of X should be x0 the second column should be x1.
Console.WriteLine()
Console.WriteLine("X =")
Console.WriteLine(X.ToTabDelimited("G5"))

' Factor a different matrix.
Dim B As FloatBandMatrix = 1.2 * A
Fact.Factor(B)
X0 = Fact.Solve(Y0)
Console.Write("Solution to Bx = y0 is ")
Console.WriteLine(X0.ToString("G3"))

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