public void FitToFunctionPolynomialCompatibilityTest()
{
// specify a cubic function
Interval r = Interval.FromEndpoints(-10.0, 10.0);
Func <double, double> fv = delegate(double x) {
return(0.0 - 1.0 * x + 2.0 * x * x - 3.0 * x * x * x);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + 0.5 * Math.Cos(x));
};
// create a data set from it
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 60);
// fit it to a cubic polynomial
UncertainMeasurementFitResult pFit = set.FitToPolynomial(3);
// fit it to a cubic polynomial
Func <double[], double, double> ff = delegate(double[] p, double x) {
return(p[0] + p[1] * x + p[2] * x * x + p[3] * x * x * x);
};
UncertainMeasurementFitResult fFit = set.FitToFunction(ff, new double[] { 0, 0, 0, 0 });
// dimension
Assert.IsTrue(pFit.Parameters.Count == fFit.Parameters.Count);
// chi squared
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.GoodnessOfFit.Statistic, fFit.GoodnessOfFit.Statistic, Math.Sqrt(TestUtilities.TargetPrecision)));
// don't demand super-high precision agreement of parameters and covariance matrix
// parameters
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters.ValuesVector, fFit.Parameters.ValuesVector, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
// covariance
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters.CovarianceMatrix, fFit.Parameters.CovarianceMatrix, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
}
public void FitDataToFunctionTest()
{
// create a data set from a nonlinear function
/*
* Interval r = Interval.FromEndpoints(-3.0, 5.0);
* double[] c = new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
* Function<double, double> fv = delegate(double x) {
* return (3.0 * Math.Cos(2.0 * Math.PI * x / 2.0 - 1.0));
* };
* Function<double, double> fu = delegate(double x) {
* return (0.1 + 0.1 * Math.Abs(x));
* };
* DataSet set = CreateDataSet(r, fv, fu, 20, 2);
*/
UncertainMeasurementSample set = new UncertainMeasurementSample();
set.Add(new UncertainMeasurement <double>(1.0, 1.0, 0.1));
set.Add(new UncertainMeasurement <double>(2.0, 0.7, 0.1));
set.Add(new UncertainMeasurement <double>(3.0, 0.0, 0.1));
set.Add(new UncertainMeasurement <double>(4.0, -0.7, 0.1));
set.Add(new UncertainMeasurement <double>(5.0, -1.0, 0.1));
set.Add(new UncertainMeasurement <double>(6.0, -0.7, 0.1));
set.Add(new UncertainMeasurement <double>(7.0, 0.0, 0.1));
set.Add(new UncertainMeasurement <double>(8.0, 0.7, 0.1));
set.Add(new UncertainMeasurement <double>(9.0, 1.0, 0.1));
// fit it to a parameterized fit function
/*
* Function<double[], double, double> ff = delegate(double[] p, double x) {
* return (p[0] * Math.Cos(2.0 * Math.PI / p[1] + p[2]));
* };
*/
Func <double[], double, double> ff = delegate(double[] p, double x) {
//Console.WriteLine(" p[0]={0}, x={1}", p[0], x);
return(p[1] * Math.Cos(x / p[0] + p[2]));
//return (x / p[0]);
};
FitResult fit = set.FitToFunction(ff, new double[] { 1.3, 1.1, 0.1 });
Console.WriteLine(fit.Parameter(0));
Console.WriteLine(fit.Parameter(1));
Console.WriteLine(fit.Parameter(2));
}
public void FitToFunctionPolynomialCompatibilityTest()
{
// specify a cubic function
Interval r = Interval.FromEndpoints(-10.0, 10.0);
Func <double, double> fv = delegate(double x) {
return(0.0 - 1.0 * x + 2.0 * x * x - 3.0 * x * x * x);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + 0.5 * Math.Cos(x));
};
// create a data set from it
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 60);
// fit it to a cubic polynomial
FitResult pFit = set.FitToPolynomial(3);
// fit it to a cubic polynomaial
Func <double[], double, double> ff = delegate(double[] p, double x) {
return(p[0] + p[1] * x + p[2] * x * x + p[3] * x * x * x);
};
FitResult fFit = set.FitToFunction(ff, new double[] { 0, 0, 0, 0 });
// the fits should agree
Console.WriteLine("{0} ?= {1}", pFit.GoodnessOfFit.Statistic, fFit.GoodnessOfFit.Statistic);
for (int i = 0; i < pFit.Dimension; i++)
{
Console.WriteLine("{0} ?= {1}", pFit.Parameter(i), fFit.Parameter(i));
Assert.IsTrue(pFit.Parameter(i).ConfidenceInterval(0.01).ClosedContains(fFit.Parameter(i).Value));
}
// dimension
Assert.IsTrue(pFit.Dimension == fFit.Dimension);
// chi squared
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.GoodnessOfFit.Statistic, fFit.GoodnessOfFit.Statistic, Math.Sqrt(TestUtilities.TargetPrecision)));
// don't demand super-high precision agreement of parameters and covariance matrix
// parameters
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters, fFit.Parameters, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
// covariance
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.CovarianceMatrix, fFit.CovarianceMatrix, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
}
