Nonlinear Curve Fitting in C# QuickStart Sample
Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class in C#.
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using System;
// The curve fitting classes reside in the
// Extreme.Mathematics.Curves namespace.
using Extreme.Mathematics.Curves;
// The predefined non-linear curves reside in the
// Extreme.Mathematics.Curves namespace.
using Extreme.Mathematics.Curves.Nonlinear;
// Vectors reside in the Extreme.Mathemaics.LinearAlgebra
// namespace
using Extreme.Mathematics;
using Extreme.Mathematics.LinearAlgebra;
namespace Extreme.Numerics.QuickStart.CSharp
{
/// <summary>
/// Illustrates nonlinear least squares curve fitting using the
/// NonlinearCurveFitter class in the
/// Extreme.Mathematics.Curves namespace of Extreme Numerics.NET.
/// </summary>
class NonlinearCurveFitting
{
static void Main(string[] args)
{
// The license is verified at runtime. We're using
// a demo license here. For more information, see
// https://numerics.net/trial-key
Extreme.License.Verify("Demo license");
// Nonlinear least squares fits are calculated using the
// NonlinearCurveFitter class:
NonlinearCurveFitter fitter = 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 vectors:
var dose = Vector.Create(1.46247, 2.3352,
4, 7, 12, 18, 23, 30, 40, 60, 90, 160, 290, 490, 860);
var 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);
var error = 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:
FourParameterLogisticCurve doseResponseCurve
= new FourParameterLogisticCurve();
// Now we set the curve fitter's Curve property:
fitter.Curve = doseResponseCurve;
// and the data values:
fitter.XValues = dose;
fitter.YValues = response;
// The GetInitialFitParameters method returns a set of
// initial values appropriate for the data:
fitter.InitialGuess = doseResponseCurve.GetInitialFitParameters(dose, response);
// The GetWeightVectorFromErrors method of the WeightFunctions
// class lets us convert the error values to weights:
fitter.WeightVector = WeightFunctions.GetWeightVectorFromErrors(error);
// The Fit method performs the actual calculation.
fitter.Fit();
// The standard deviations associated with each parameter
// are available through the GetStandardDeviations method.
var 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
fitter = new NonlinearCurveFitter();
// Here, we need to define our own curve.
// The MyCurve class is defined below.
fitter.Curve = new MyCurve();
// You can use Automatic Differentiation to compute
// the derivative of the function and the partial derivatives
// with respect to the curve parameters.
// To do so, call the FromExpression method of the NonlinearCurve
// class with a lambda expression for the value of the function.
// The first argument of the lambda is the x value. The remaining
// arguments correspond to the curve parameters:
fitter.Curve = NonlinearCurve.FromExpression((x, a, b, c) => a * Math.Exp(b / (x + c)));
// In this case, we have to specify the initial values
// for the parameters:
fitter.InitialGuess = Vector.Create(0.2, 40000, 2500);
// The data is provided as vectors.
// X values go into the XValues property...
fitter.XValues = Vector.Create(new double[]
{
5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01,
7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01,
9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02,
1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02,
});
// ...and Y values go into the YValues property:
fitter.YValues = Vector.Create(new double[]
{
3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04,
1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03,
8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03,
4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03
});
fitter.WeightVector = null;
// 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.
var 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}", 5.6096364710E-03, 1.5687892471E-04 );
Console.WriteLine("b2: {0,20} {1,20}", 6.1813463463E+03, 2.3309021107E+01 );
Console.WriteLine("b3: {0,20} {1,20}", 3.4522363462E+02, 7.8486103508E-01 );
// 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.OneOverX;
// 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();
}
}
// 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 : NonlinearCurve
{
// Call the base constructor with the number of
// parameters.
public MyCurve() : base(3)
{
// It is convenient to set common starting values
// for the curve parameters in the constructor:
this.Parameters[0] = 0.2;
this.Parameters[1] = 40000;
this.Parameters[2] = 2500;
}
// The ValueAt method evaluates the function:
override public double ValueAt(double x)
{
return Parameters[0] * Math.Exp(Parameters[1] / (x + Parameters[2]));
}
// The SlopeAt method evaluates the derivative:
override public double SlopeAt(double x)
{
return Parameters[0] * Parameters[1] * Math.Exp(Parameters[1] / (x + Parameters[2]))
/ Math.Pow(x + Parameters[2], 2);
}
// 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.
override public void FillPartialDerivatives(double x, DenseVector<double> f)
{
double exp = 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);
}
}
}