VB Least Squares Example

Imports System
Imports System.Globalization
Imports System.Threading

Imports CenterSpace.NMath.Core

Namespace CenterSpace.NMath.Core.Examples.VisualBasic

  ' A .NET example in Visual Basic showing how to use the least squares classes to solve 
  ' linear least squares problems.
  Module LeastSquaresExample

    Sub Main()

      Dim Original As CultureInfo = Thread.CurrentThread.CurrentCulture

      ' This example uses strings representing numbers in the US locale
      ' so change the current culture info.  For example, "$4.30"
      Thread.CurrentThread.CurrentCulture = New CultureInfo("en-US")

      ' Calculate the slope and intercept of the linear least squares fit
      ' through the five points:
      ' (20, .446) (30, .601), (40, .786), (50, .928), (60, .950)
      Dim A As New DoubleMatrix("5x1[20.0  30.0  40.0  50.0  60.0]")
      Dim Y As New DoubleVector("[.446 .601 .786 .928 .950]")

      ' Back to original culture
      Thread.CurrentThread.CurrentCulture = Original

      ' We want our straight line to be of the form y = mx + b, where b is
      ' not necessarily equal to zero. Thus we will set the third 
      ' constructor argument to true so that we calculate the intercept
      ' parameter. 
      Dim Lsq As New DoubleLeastSquares(A, Y, True)

      Console.WriteLine()
      Console.WriteLine()
      Console.WriteLine("Y-intercept = {0}", Lsq.X(0))
      Console.WriteLine("Slope = {0}", Lsq.X(1))

      ' We can look at the residuals which are the difference between the 
      ' actual value of y at a point x, and the corresponding point y on 
      ' line for the same x.
      Console.WriteLine("Residuals = {0}", Lsq.Residuals.ToString("F3"))

      ' Finally, we can look at the residual sum of squares, which is the
      ' sum of the squares of the elements in the residual vector.
      Console.WriteLine("Residual Sum of Squares (RSS) = {0}", Lsq.ResidualSumOfSquares.ToString("F3"))

      ' The least squares class can also be used to solve "rank-deficient" least 
      ' square problems:
      A = New DoubleMatrix("6x4 [0 9 -6 3  -3 0 -3 0  1 3 -1 1  1 3 -1 1  -2 0 -2 0  3 6 -1 2]")
      Y = New DoubleVector("[-3 5 -2 2 1 -2]")

      ' For this problem we will specify a tolerance for computing the effective rank
      ' of the matrix A, and we will not have the class add an intercept parameter
      ' for us.
      Lsq = New DoubleLeastSquares(A, Y, 0.0000000001)
      Console.WriteLine("Least squares solution = {0}", Lsq.X.ToString("F3"))
      Console.Write("Rank computed using a tolerance of ")
      Console.Write(Lsq.Tolerance.ToString() + ", = ")
      Console.WriteLine(Lsq.Rank.ToString())

      ' You can even use the least squares class to solve under-determined systems
      ' (the case where A has more columns than rows).
      A = New DoubleMatrix("6x4 [-3 -1 6 -5  5 4 -6 8  7 5 0 -4  -7 4 0 3  -7 7 -8 2  3 4 2 -4]")
      Y = New DoubleVector("[-3 1 8 -2]")
      Lsq = New DoubleLeastSquares(A.Transpose(), Y, 0.00000001)

      Console.Write("Solution to under-determined system = ")
      Console.WriteLine(Lsq.X.ToString("F3"))

      Console.Write("Rank computed using a tolerance of ")
      Console.Write(Lsq.Tolerance.ToString() + " is ")
      Console.WriteLine(Lsq.Rank.ToString())

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

    End Sub
  End Module
End Namespace