public void FitDataToLineUncertaintyTest()
{
double[] xs = TestUtilities.GenerateUniformRealValues(0.0, 10.0, 10);
Func <double, double> fv = delegate(double x) {
return(2.0 * x - 1.0);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + x);
};
MultivariateSample sample = new MultivariateSample(2);
SymmetricMatrix covariance = new SymmetricMatrix(2);
// create a bunch of small data sets
for (int i = 0; i < 100; i++)
{
UncertainMeasurementSample data = CreateDataSet(xs, fv, fu, i);
FitResult fit = data.FitToLine();
sample.Add(fit.Parameters);
covariance = fit.CovarianceMatrix;
// because it depends only on the x's and sigmas, the covariance is always the same
Console.WriteLine("cov_00 = {0}", covariance[0, 0]);
}
// the measured covariances should agree with the claimed covariances
//Assert.IsTrue(sample.PopulationCovariance(0,0).ConfidenceInterval(0.95).ClosedContains(covariance[0,0]));
//Assert.IsTrue(sample.PopulationCovariance(0,1).ConfidenceInterval(0.95).ClosedContains(covariance[0,1]));
//Assert.IsTrue(sample.PopulationCovariance(1,0).ConfidenceInterval(0.95).ClosedContains(covariance[1,0]));
//Assert.IsTrue(sample.PopulationCovariance(1,1).ConfidenceInterval(0.95).ClosedContains(covariance[1,1]));
}
public void FitDataToLineChiSquaredTest()
{
// we want to make sure that the chi^2 values we are producing from line fits are distributed as expected
// create a sample to hold chi^2 values
Sample chis = new Sample();
// define a model
Interval r = Interval.FromEndpoints(-5.0, 5.0);
Func <double, double> fv = delegate(double x) {
return(1.0 - 2.0 * x);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + 0.5 * Math.Sin(x));
};
// draw 50 data sets from the model and fit year
// store the resulting chi^2 value in the chi^2 set
for (int i = 0; i < 50; i++)
{
UncertainMeasurementSample xs = CreateDataSet(r, fv, fu, 10, i);
FitResult fit = xs.FitToLine();
double chi = fit.GoodnessOfFit.Statistic;
chis.Add(chi);
}
// sanity check the sample
Assert.IsTrue(chis.Count == 50);
// test whether the chi^2 values are distributed as expected
ContinuousDistribution chiDistribution = new ChiSquaredDistribution(8);
TestResult ks = chis.KolmogorovSmirnovTest(chiDistribution);
Assert.IsTrue(ks.LeftProbability < 0.95);
}
public void FitDataToProportionalityTest()
{
Interval r = Interval.FromEndpoints(0.0, 0.1);
Func <double, double> fv = delegate(double x) {
return(0.5 * x);
};
Func <double, double> fu = delegate(double x) {
return(0.02);
};
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 20);
// fit to proportionality
FitResult prop = set.FitToProportionality();
Assert.IsTrue(prop.Dimension == 1);
Assert.IsTrue(prop.Parameter(0).ConfidenceInterval(0.95).ClosedContains(0.5));
Assert.IsTrue(prop.GoodnessOfFit.LeftProbability < 0.95);
// fit to line
FitResult line = set.FitToLine();
Assert.IsTrue(line.Dimension == 2);
// line's intercept should be compatible with zero and slope with proportionality constant
Assert.IsTrue(line.Parameter(0).ConfidenceInterval(0.95).ClosedContains(0.0));
Assert.IsTrue(line.Parameter(1).ConfidenceInterval(0.95).ClosedContains(prop.Parameter(0).Value));
// the fit should be better, but not too much better
Assert.IsTrue(line.GoodnessOfFit.Statistic < prop.GoodnessOfFit.Statistic);
}
public void FitToFunctionLinearCompatibilityTest()
{
// specify a cubic function
Interval r = Interval.FromEndpoints(-5.0, 5.0);
Func <double, double> fv = delegate(double x) {
return(1.0 + 2.0 * 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.Sin(x));
};
// create a data set from it
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 30);
// fit it to a cubic polynomial
UncertainMeasurementFitResult pFit = set.FitToLine();
//FitResult 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);
//return (p[0] + p[1] * x + p[2] * x * x + p[3] * x * x * x);
};
UncertainMeasurementFitResult fFit = set.FitToFunction(ff, new double[] { 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)));
// parameters
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters.ValuesVector, fFit.Parameters.ValuesVector, Math.Sqrt(TestUtilities.TargetPrecision)));
// covariance
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters.CovarianceMatrix, fFit.Parameters.CovarianceMatrix, Math.Sqrt(TestUtilities.TargetPrecision)));
}
public void FitDataToLineTest()
{
Interval r = Interval.FromEndpoints(0.0, 10.0);
Func <double, double> fv = delegate(double x) {
return(2.0 * x - 1.0);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + x);
};
UncertainMeasurementSample data = CreateDataSet(r, fv, fu, 20);
// sanity check the data set
Assert.IsTrue(data.Count == 20);
// fit to a line
FitResult line = data.FitToLine();
Assert.IsTrue(line.Dimension == 2);
Assert.IsTrue(line.Parameter(0).ConfidenceInterval(0.95).ClosedContains(-1.0));
Assert.IsTrue(line.Parameter(1).ConfidenceInterval(0.95).ClosedContains(2.0));
Assert.IsTrue(line.GoodnessOfFit.LeftProbability < 0.95);
// correlation coefficient should be related to covariance as expected
Assert.IsTrue(TestUtilities.IsNearlyEqual(line.CorrelationCoefficient(0, 1), line.Covariance(0, 1) / line.Parameter(0).Uncertainty / line.Parameter(1).Uncertainty));
// fit to a 1st order polynomial and make sure it agrees
FitResult poly = data.FitToPolynomial(1);
Assert.IsTrue(poly.Dimension == 2);
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.Parameters, line.Parameters));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.CovarianceMatrix, line.CovarianceMatrix));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.Statistic, line.GoodnessOfFit.Statistic));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.LeftProbability, line.GoodnessOfFit.LeftProbability));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.RightProbability, line.GoodnessOfFit.RightProbability));
// fit to a constant; the result should be poor
FitResult constant = data.FitToConstant();
Assert.IsTrue(constant.GoodnessOfFit.LeftProbability > 0.95);
}