New Version 6.0!

Try it for free with our fully functional 60-day trial version.

Download now!

QuickStart Samples

Nonlinear Curve Fitting QuickStart Sample (Visual Basic)

Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class in Visual Basic.

C# code F# code IronPython code Back to QuickStart Samples

Option Infer On

' The curve fitting classes reside in the 
' Extreme.Mathematics.Curves namespace.
Imports Extreme.Mathematics.Curves
' The predefined non-linear curves reside in the 
' Extreme.Mathematics.Curves namespace.
Imports Extreme.Mathematics.Curves.Nonlinear
' Vectors reside in the Extreme.Mathemaics.LinearAlgebra
' namespace
Imports Extreme.Mathematics
Imports Extreme.Mathematics.Algorithms
Imports Extreme.Mathematics.LinearAlgebra

Namespace Extreme.Numerics.QuickStart.VB
    ' Illustrates nonlinear least squares curve fitting using the
    ' NonlinearCurveFitter class in the 
    ' Extreme.Mathematics.Curves namespace of the Extreme
    ' Optimization Numerical Libraries for .NET.
    Module NonlinearCurveFitting

        Sub Main()

            ' Nonlinear least squares fits are calculated using the
            ' NonlinearCurveFitter class:
            Dim fitter As New NonlinearCurveFitter

            ' In the first example, we fit a dose response curve
            ' to a data set that includes error information.

            ' The data points must be supplied as Vector objects:
            Dim dose = Vector.Create(1.46247, 2.3352,
                4, 7, 12, 18, 23, 30, 40, 60, 90, 160, 290, 490, 860)
            Dim response = Vector.Create(95.49073, 95.14551, 94.86448,
                92.66762, 85.36377, 74.72183, 62.76747, 51.04137, 38.20257,
                28.01712, 19.40086, 13.18117, 9.87161, 7.64622, 7.21826)
            Dim errors = Vector.Create(4.74322, 4.74322, 4.74322,
                4.63338, 4.26819, 3.73609, 3.13837, 3.55207, 3.91013,
                2.40086, 2.6, 3.65906, 2.49358, 2.38231, 2.36091)

            ' You must supply the curve whose parameters will be
            ' fit to the data. The curve must inherit from NonlinearCurve.
            ' The FourParameterLogistic curve is one of several
            ' predefined nonlinear curves:
            Dim doseResponseCurve As FourParameterLogisticCurve _
                = New FourParameterLogisticCurve

            ' Now we set the curve fitter's Curve property:
            fitter.Curve = doseResponseCurve
            ' The GetInitialFitParameters method computes
            ' initial values appropriate for the data:
            fitter.InitialGuess = doseResponseCurve.GetInitialFitParameters(dose, response)

            ' and the data values:
            fitter.XValues = dose
            fitter.YValues = response
            ' The GetWeightVectorFromErrors method of the WeightFunctions
            ' class lets us convert the error values to weights:
            fitter.WeightVector = WeightFunctions.GetWeightVectorFromErrors(errors)

            ' The Fit method performs the actual calculation.
            fitter.Fit()
            ' The standard deviations associated with each parameter
            ' are available through the GetStandardDeviations method.
            Dim s = fitter.GetStandardDeviations()

            ' We can now print the results:
            Console.WriteLine("Dose response curve")

            Console.WriteLine("Initial value: {0,10:F6} +/- {1:F4}", doseResponseCurve.InitialValue, s(0))
            Console.WriteLine("Final value:   {0,10:F6} +/- {1:F4}", doseResponseCurve.FinalValue, s(1))
            Console.WriteLine("Center:        {0,10:F6} +/- {1:F4}", doseResponseCurve.Center, s(2))
            Console.WriteLine("Hill slope:    {0,10:F6} +/- {1:F4}", doseResponseCurve.HillSlope, s(3))

            ' We can also show some statistics about the calculation:
            Console.WriteLine("Residual sum of squares: {0}", fitter.Residuals.Norm())
            ' The Optimizer property returns the MultidimensionalOptimization object
            ' used to perform the calculation:
            Console.WriteLine("# iterations: {0}", fitter.Optimizer.IterationsNeeded)
            Console.WriteLine("# function evaluations: {0}", fitter.Optimizer.EvaluationsNeeded)

            Console.WriteLine()

            '
            ' Defining your own nonlinear curve
            '

            ' In this example, we use one of the datasets (MGH10) 
            ' from the National Institute for Statistics and Technology
            ' (NIST) Statistical Reference Datasets.
            ' See http://www.itl.nist.gov/div898/strd for details

            ' Here, we need to define our own curve.
            ' The MyCurve class is defined below.
            fitter.Curve = New MyCurve
#If NET40 Then
#End If

            ' The data is provided as Vector objects.
            ' X values go into the XValues property...
            fitter.XValues = Vector.Create(
                50.0, 55.0, 60.0, 65.0,
                70.0, 75.0, 80.0, 85.0,
                90.0, 95.0, 100.0, 105.0,
                110.0, 115.0, 120.0, 125.0)
            ' ...and Y values go into the YValues property:
            fitter.YValues = Vector.Create(
                34780.0, 28610.0, 23650.0, 19630.0,
                16370.0, 13720.0, 11540.0, 9744.0,
                8261.0, 7030.0, 6005.0, 5147.0,
                4427.0, 3820.0, 3307.0, 2872.0)

            fitter.WeightVector = Nothing
            ' The Fit method performs the actual calculation:
            fitter.Fit()

            ' A Vector containing the parameters of the best fit
            ' can be obtained through the
            ' BestFitParameters property.
            Dim solution = fitter.BestFitParameters
            s = fitter.GetStandardDeviations()

            Console.WriteLine("NIST Reference Data Set")
            Console.WriteLine("Solution:")
            Console.WriteLine("b1: {0,20} {1,20}", solution(0), s(0))
            Console.WriteLine("b2: {0,20} {1,20}", solution(1), s(1))
            Console.WriteLine("b3: {0,20} {1,20}", solution(2), s(2))

            Console.WriteLine("Certified values:")
            Console.WriteLine("b1: {0,20} {1,20}", 0.005609636471, 0.00015687892471)
            Console.WriteLine("b2: {0,20} {1,20}", 6181.3463463, 23.309021107)
            Console.WriteLine("b3: {0,20} {1,20}", 345.22363462, 0.78486103508)

            ' Now let's redo the same operation, but with observations weighted
            ' by 1/Y^2. To do this, we set the WeightFunction property.
            ' The WeightFunctions class defines a set of ready-to-use weight functions.
            fitter.WeightFunction = WeightFunctions.OneOverYSquared
            ' Refit the curve:
            fitter.Fit()
            solution = fitter.BestFitParameters
            s = fitter.GetStandardDeviations()

            ' The solution is slightly different:
            Console.WriteLine("Solution (weighted observations):")
            Console.WriteLine("b1: {0,20} {1,20}", solution(0), s(0))
            Console.WriteLine("b2: {0,20} {1,20}", solution(1), s(1))
            Console.WriteLine("b3: {0,20} {1,20}", solution(2), s(2))

            Console.Write("Press Enter key to exit...")
            Console.ReadLine()
        End Sub


        ' This is our nonlinear curve implementation. For details, see 
        ' http:'www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml
        ' You must inherit from NonlinearCurve:
        Public Class MyCurve : Inherits NonlinearCurve
            ' Call the base constructor with the number of
            ' parameters.
            Public Sub New()
                MyBase.New(3)
                ' It is convenient to set common starting values
                ' for the curve parameters in the constructor:
                Me.Parameters(0) = 0.2
                Me.Parameters(1) = 40000
                Me.Parameters(2) = 2500
            End Sub

            ' The ValueAt method evaluates the function:
            Public Overrides Function ValueAt(ByVal x As Double) As Double
                Return Parameters(0) * Math.Exp(Parameters(1) / (x + Parameters(2)))
            End Function

            ' The SlopeAt method evaluates the derivative:
            Public Overrides Function SlopeAt(ByVal x As Double) As Double
                Return Parameters(0) * Parameters(1) * Math.Exp(Parameters(1) / (x + Parameters(2))) _
                 / Math.Pow(x + Parameters(2), 2)
            End Function

            ' The FillPartialDerivatives evaluates the partial derivatives
            ' with respect to the curve parameters, and returns
            ' the result in a vector. If you don't supply this method, 
            ' a numerical approximation is used.
            Public Overrides Sub FillPartialDerivatives(x As Double, f As DenseVector(Of Double))
                Dim exp As Double = Math.Exp(Parameters(1) / (x + Parameters(2)))
                f(0) = exp
                f(1) = Parameters(0) * exp / (x + Parameters(2))
                f(2) = -Parameters(0) * Parameters(1) * exp / Math.Pow(x + Parameters(2), 2)
            End Sub

        End Class

    End Module

End Namespace