[SerializableAttribute]
public class BoundedMultiVariableFunctionFitter<M> : MultiVariableFunctionFitter<M>
where M : new(), IBoundedNonlinearLeastSqMinimizer

<SerializableAttribute> _
Public Class BoundedMultiVariableFunctionFitter(Of M As {New, IBoundedNonlinearLeastSqMinimizer}) _
	Inherits MultiVariableFunctionFitter(Of M)

[SerializableAttribute]
generic<typename M>
where M : gcnew(), IBoundedNonlinearLeastSqMinimizer
public ref class BoundedMultiVariableFunctionFitter : public MultiVariableFunctionFitter<M>

In the space of the function parameters, begining at a specified starting point, finds a minimum (possibly local) in the sum of the squared residuals with respect to a set of data points subject to the supplied inequality constraints on the parameters. You must supply at least as many data points to fit as your function has parameters.
For example, the following code fits a function of the form data to the following function:

            F(p, x) = p[0]x[0]x[1]^2 + p[1]sin(x[0]) + p[2]x[1]^3;
            

to a set of 10 data points, beginning at point (1, 1, 1) in the parameter space. and satisfying the parameter constraints 0 < p[0] < 100 0 < p[1] < 50 0 < p[2] < 75

CopyC#

DoubleMatrix x = new DoubleMatrix(10, 2);
x[Slice.All, 0] = new DoubleVector("3.6 7.7 9.3 4.1 8.6 2.8 1.3 7.9 10.0 5.4");
x[Slice.All, 1] = new DoubleVector("16.5 150.6 263.1 24.7 208.5 9.9 2.7 163.9 325.0 54.3");
DoubleVector upperBounds = new DoubleVector("100, 50, 75");
DoubleVector lowerBounds = new DoubleVector("0 0 0");
DoubleVector yValues = new DoubleVector("95.09 23.11 60.63 48.59 89.12 76.97 45.68 1.84 82.17 44.47");
DoubleVector initialParameters = new DoubleVector("10 10 10");


Func<DoubleVector, DoubleVector, double> f = delegate(DoubleVector p, DoubleVector xdata)
{
  return Math.Pow(p[0] * xdata[0] * xdata[1], 2.0) + p[1] * Math.Sin(xdata[0]) + Math.Pow(p[2] * xdata[1], 3.0);
};


MultiVariableFunctionFitter<TrustRegionMinimizer> fitter = new MultiVariableFunctionFitter<TrustRegionMinimizer>(f);
DoubleVector solution = fitter.Fit(x, yValues, initialParameters, lowerBounds, upperBounds);

Note that problems can have multiple local minima. Trying different initial parameter points is recommended for better solutions. Also, the initial parameter should satisfy the parameter constraints.

System..::.Object
  CenterSpace.NMath.Analysis..::.MultiVariableFunctionFitter<(Of <(M>)>)
    CenterSpace.NMath.Analysis..::.BoundedMultiVariableFunctionFitter<(Of <(M>)>)