public void TestGaussKronrodRuleIntegration(int order)
{
double appoximateArea = GaussKronrodRule.Integrate(TargetFunctionA, StartA, StopA, out _, out _, order: order);
double relativeError = Math.Abs(TargetAreaA - appoximateArea) / TargetAreaA;
Assert.Less(relativeError, 5e-16);
}
/// <summary>
/// Approximation of the definite integral of an analytic smooth function by Gauss-Kronrod quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.
/// </summary>
/// <param name="f">The analytic smooth complex function to integrate, defined on the real domain.</param>
/// <param name="intervalBegin">Where the interval starts.</param>
/// <param name="intervalEnd">Where the interval stops.</param>
/// <param name="error">The difference between the (N-1)/2 point Gauss approximation and the N-point Gauss-Kronrod approximation</param>
/// <param name="L1Norm">The L1 norm of the result, if there is a significant difference between this and the returned value, then the result is likely to be ill-conditioned.</param>
/// <param name="targetRelativeError">The expected relative accuracy of the approximation.</param>
/// <param name="maximumDepth">The maximum number of interval splittings permitted before stopping</param>
/// <param name="order">The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points</param>
/// <returns>Approximation of the finite integral in the given interval.</returns>
public static Complex GaussKronrod(Func <double, Complex> f, double intervalBegin, double intervalEnd, out double error, out double L1Norm, double targetRelativeError = 1E-8, int maximumDepth = 15, int order = 15)
{
return(GaussKronrodRule.ContourIntegrate(f, intervalBegin, intervalEnd, out error, out L1Norm, targetRelativeError: targetRelativeError, maximumDepth: maximumDepth, order: order));
}
/// <summary>
/// Approximation of the definite integral of an analytic smooth function by Gauss-Kronrod quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.
/// </summary>
/// <param name="f">The analytic smooth function to integrate.</param>
/// <param name="intervalBegin">Where the interval starts.</param>
/// <param name="intervalEnd">Where the interval stops.</param>
/// <param name="targetRelativeError">The expected relative accuracy of the approximation.</param>
/// <param name="maximumDepth">The maximum number of interval splittings permitted before stopping.</param>
/// <param name="order">The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points.</param>
/// <returns>Approximation of the finite integral in the given interval.</returns>
public static double GaussKronrod(Func <double, double> f, double intervalBegin, double intervalEnd, double targetRelativeError = 1E-8, int maximumDepth = 15, int order = 15)
{
return(GaussKronrodRule.Integrate(f, intervalBegin, intervalEnd, out _, out _, targetRelativeError: targetRelativeError, maximumDepth: maximumDepth, order: order));
}
