# VB Iteratively Reweighted Least Sq Example

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```ï»¿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 classes for solving iteratively reweighted
' least squares problems.
Module IterativelyReweightedLeastSqExample

Sub Main()

' Set up a least squares problem, Ax = b, with random data.
Dim RNG As New RandGenUniform(-2, 2, 124)
Dim Rows As Integer = 10
Dim Cols As Integer = 2
Dim A As New DoubleMatrix(Rows, Cols, RNG)
Dim X As New DoubleVector(Cols, RNG)
' Fix up the right hand side b so that x
' is the exact solution, then throw in some outliers.
Dim B As DoubleVector = NMathFunctions.Product(A, X)
' Throw in a few outliers...
B(1) = 23
B(4) = -10

' Create an iteratively reweighted least squares instance
' and use it to solve the problem using the default settings.
' The default weighting is DoubleBisquareWeightingFunction which
' uses the bisquare weighting algorithm.
Dim Irls As New DoubleIterativelyReweightedLeastSq()

' Solve. The third parameter below specifies prepending a column of ones to the
' data in A representing a constant term in the model (which should come out
' to be zero in the solution from the way we cooked the data). Note that our
' input matrix A will not actually be changed.
Dim Solution As DoubleVector = Irls.Solve(A, B, True)

Console.WriteLine()
Console.WriteLine("Solution with bisquare weighting")
Console.WriteLine(Solution.ToString("G5"))
Console.WriteLine()
Console.WriteLine("||residuals|| = " & Irls.Residuals.TwoNorm())
Console.WriteLine()
If (Irls.Iterations >= Irls.MaxIterations) Then
Console.WriteLine("The algorithm did not converge in {0} iterations.", Irls.MaxIterations)
Else
Console.WriteLine("Algorithm converged in {0} iterations.", Irls.Iterations)
End If

' Change some of the settings that control the iteration.
Irls.MaxIterations = 300
Irls.Tolerance = 0.0000001

' The convergence function is a delegate that may specified by the user for
' determining if the algorithm has converged and iteration terminated. The
' delegate takes as arguments the previous and current solutions and residuals
' and the tolerance and returns a bool. See the ResidualsChanged function
' below.
Dim ResidualsUnchanged As New DoubleIterativelyReweightedLeastSq.ToleranceMetFunction(AddressOf ResidualsUnchangedFunction)
Irls.ConvergenceFunction = ResidualsUnchanged

' Change the weighting function used from the default bisquare weighting to the
' fair weighting function. See the class DoubleFairWeightingFunction for
' particulars.
Irls.WeightsFunction = New DoubleFairWeightingFunction()

' Solve the problem with the new settings.
Solution = Irls.Solve(A, B, True)

Console.WriteLine()
Console.WriteLine("Solution with fair weighting")
Console.WriteLine(Solution.ToString("G5"))
Console.WriteLine()
Console.WriteLine("||residuals|| = " & Irls.Residuals.TwoNorm())
Console.WriteLine()
If (Irls.Iterations >= Irls.MaxIterations) Then
Console.WriteLine("The algorithm did not converge in {0} iterations.", Irls.MaxIterations)
Else
Console.WriteLine("Algorithm converged in {0} iterations.", Irls.Iterations)
End If

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

End Sub

' Convergence function for use in the iteratively reweighted least squares
' algorithm. This particular convergence function returns true when the residuals
' from the current iterations are relatively the same as the residuals in the
' previous iteration.
Private Function ResidualsUnchangedFunction(ByVal Tolerance As Double, ByVal LastSolution As DoubleVector, _
ByVal CurrenSolution As DoubleVector, ByVal LastResiduals As DoubleVector, ByVal CurrentResiduals As DoubleVector) As Boolean

Dim MaxAbsDiff As Double = NMathFunctions.MaxAbsValue(CurrentResiduals - LastResiduals)
Return (MaxAbsDiff / NMathFunctions.MaxAbsValue(CurrentResiduals)) < Tolerance

End Function

End Module
End Namespace

```
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