public void BivariateNonlinearFitSimple()
{
double t0 = 3.0;
double s0 = 1.0;
ContinuousDistribution xDistribution = new CauchyDistribution(0.0, 2.0);
ContinuousDistribution eDistribution = new NormalDistribution(0.0, 0.5);
Random rng = new Random(5);
List <double> x = TestUtilities.CreateDataSample(rng, xDistribution, 48).ToList();
List <double> y = x.Select(z => Math.Sin(2.0 * Math.PI * z / t0 + s0) + eDistribution.GetRandomValue(rng)).ToList();
Func <IReadOnlyDictionary <string, double>, double, double> fitFunction = (d, z) => {
double t = d["Period"];
double s = d["Phase"];
return(Math.Sin(2.0 * Math.PI * z / t + s));
};
Dictionary <string, double> start = new Dictionary <string, double>()
{
{ "Period", 2.5 }, { "Phase", 1.5 }
};
NonlinearRegressionResult result = y.NonlinearRegression(x, fitFunction, start);
Assert.IsTrue(result.Parameters["Period"].Estimate.ConfidenceInterval(0.99).ClosedContains(t0));
Assert.IsTrue(result.Parameters["Phase"].Estimate.ConfidenceInterval(0.99).ClosedContains(s0));
for (int i = 0; i < x.Count; i++)
{
double yp = result.Predict(x[i]);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Residuals[i], y[i] - yp));
}
}
public void Bug53()
{
// User sent data for which non-linear fit failed with Nonconvergence exception.
List <double> x = new List <double>();
List <double> y = new List <double>();
using (System.IO.StreamReader reader = System.IO.File.OpenText(@"Bug53.txt")) {
reader.ReadLine();
while (!reader.EndOfStream)
{
string line = reader.ReadLine();
string[] values = line.Split(';');
y.Add(Double.Parse(values[0]));
x.Add(Double.Parse(values[1]));
}
}
NonlinearRegressionResult r = y.NonlinearRegression(
x,
(IReadOnlyDictionary <string, double> p, double u) => {
return(p["0"] * (1.0 - Math.Exp(-p["1"] * (u - p["2"]))));
},
//new Dictionary<string, double>() { { "0", 100.0 }, { "1", 1.0 }, { "2", 1.0 } }
new Dictionary <string, double>()
{
{ "0", 1.0 }, { "1", 1.0 }, { "2", 0.0 }
}
);
}
public void BivariateNonlinearFitVariances()
{
// Verify that we can fit a non-linear function,
// that the estimated parameters do cluster around the true values,
// and that the estimated parameter covariances do reflect the actually observed covariances
double a = 2.7;
double b = 3.1;
ContinuousDistribution xDistribution = new ExponentialDistribution(2.0);
ContinuousDistribution eDistribution = new NormalDistribution(0.0, 4.0);
FrameTable parameters = new FrameTable();
parameters.AddColumns <double>("a", "b");
MultivariateSample covariances = new MultivariateSample(3);
for (int i = 0; i < 64; i++)
{
BivariateSample sample = new BivariateSample();
Random rng = new Random(i);
for (int j = 0; j < 8; j++)
{
double x = xDistribution.GetRandomValue(rng);
double y = a * Math.Pow(x, b) + eDistribution.GetRandomValue(rng);
sample.Add(x, y);
}
NonlinearRegressionResult fit = sample.NonlinearRegression(
(IReadOnlyList <double> p, double x) => p[0] * Math.Pow(x, p[1]),
new double[] { 1.0, 1.0 }
);
parameters.AddRow(fit.Parameters.ValuesVector);
covariances.Add(fit.Parameters.CovarianceMatrix[0, 0], fit.Parameters.CovarianceMatrix[1, 1], fit.Parameters.CovarianceMatrix[0, 1]);
}
Assert.IsTrue(parameters["a"].As <double>().PopulationMean().ConfidenceInterval(0.99).ClosedContains(a));
Assert.IsTrue(parameters["b"].As <double>().PopulationMean().ConfidenceInterval(0.99).ClosedContains(b));
Assert.IsTrue(parameters["a"].As <double>().PopulationVariance().ConfidenceInterval(0.99).ClosedContains(covariances.Column(0).Mean));
Assert.IsTrue(parameters["b"].As <double>().PopulationVariance().ConfidenceInterval(0.99).ClosedContains(covariances.Column(1).Mean));
Assert.IsTrue(parameters["a"].As <double>().PopulationCovariance(parameters["b"].As <double>()).ConfidenceInterval(0.99).ClosedContains(covariances.Column(2).Mean));
Assert.IsTrue(Bivariate.PopulationCovariance(parameters["a"].As <double>(), parameters["b"].As <double>()).ConfidenceInterval(0.99).ClosedContains(covariances.Column(2).Mean));
}
