/// <summary>
/// Fits the data to an arbitrary parameterized function.
/// </summary>
/// <param name="function">The fit function.</param>
/// <param name="start">An initial guess at the parameters.</param>
/// <returns>A fit result containing the best-fitting function parameters
/// and a χ<sup>2</sup> test of the quality of the fit.</returns>
/// <exception cref="ArgumentNullException"><paramref name="function"/> or <paramref name="start"/> are <see langword="null"/>.</exception>
/// <exception cref="InsufficientDataException">There are fewer data points than fit parameters.</exception>
/// <exception cref="DivideByZeroException">The curvature matrix is singular, indicating that the data is independent of
/// one or more parameters, or that two or more parameters are linearly dependent.</exception>
public FitResult FitToFunction(Func <double[], T, double> function, double[] start)
{
if (function == null)
{
throw new ArgumentNullException(nameof(function));
}
if (start == null)
{
throw new ArgumentNullException(nameof(start));
}
// you can't do a fit with less data than parameters
if (this.Count < start.Length)
{
throw new InsufficientDataException();
}
/*
* Func<IList<double>, double> function0 = (IList<double> x0) => {
* double[] x = new double[x0.Count];
* x0.CopyTo(x, 0);
* return(function(x));
* };
* MultiExtremum minimum0 = MultiFunctionMath.FindMinimum(function0, start);
*/
// create a chi^2 fit metric and minimize it
FitMetric <T> metric = new FitMetric <T>(this, function);
SpaceExtremum minimum = FunctionMath.FindMinimum(new Func <double[], double>(metric.Evaluate), start);
// compute the covariance (Hessian) matrix by inverting the curvature matrix
SymmetricMatrix A = 0.5 * minimum.Curvature();
CholeskyDecomposition CD = A.CholeskyDecomposition(); // should not return null if we were at a minimum
if (CD == null)
{
throw new DivideByZeroException();
}
SymmetricMatrix C = CD.Inverse();
// package up the results and return them
TestResult test = new TestResult("ChiSquare", minimum.Value, TestType.RightTailed, new ChiSquaredDistribution(this.Count - minimum.Dimension));
FitResult fit = new FitResult(minimum.Location(), C, test);
return(fit);
}
/// <summary>
/// Fits the data to an arbitrary parameterized function.
/// </summary>
/// <param name="function">The fit function.</param>
/// <param name="start">An initial guess at the parameters.</param>
/// <returns>A fit result containing the best-fitting function parameters
/// and a χ<sup>2</sup> test of the quality of the fit.</returns>
/// <exception cref="ArgumentNullException"><paramref name="function"/> or <paramref name="start"/> are <see langword="null"/>.</exception>
/// <exception cref="InsufficientDataException">There are fewer data points than fit parameters.</exception>
/// <exception cref="DivideByZeroException">The curvature matrix is singular, indicating that the data is independent of
/// one or more parameters, or that two or more parameters are linearly dependent.</exception>
public UncertainMeasurementFitResult FitToFunction(Func <double[], T, double> function, double[] start)
{
if (function == null)
{
throw new ArgumentNullException(nameof(function));
}
if (start == null)
{
throw new ArgumentNullException(nameof(start));
}
// you can't do a fit with less data than parameters
if (this.Count < start.Length)
{
throw new InsufficientDataException();
}
// create a chi^2 fit metric and minimize it
FitMetric <T> metric = new FitMetric <T>(this, function);
SpaceExtremum minimum = FunctionMath.FindMinimum(new Func <double[], double>(metric.Evaluate), start);
// compute the covariance (Hessian) matrix by inverting the curvature matrix
SymmetricMatrix A = 0.5 * minimum.Curvature();
CholeskyDecomposition CD = A.CholeskyDecomposition(); // should not return null if we were at a minimum
if (CD == null)
{
throw new DivideByZeroException();
}
SymmetricMatrix C = CD.Inverse();
// package up the results and return them
TestResult test = new TestResult("χ²", minimum.Value, new ChiSquaredDistribution(this.Count - minimum.Dimension), TestType.RightTailed);
ParameterCollection parameters = new ParameterCollection(NumberNames(start.Length), new ColumnVector(minimum.Location(), 0, 1, start.Length, true), C);
return(new UncertainMeasurementFitResult(parameters, test));
}
