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IntegrateGaussKronrod(FuncDouble, Double, Double, Double, Double, Double, Double, Int32, Int32) Method

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.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public static double GaussKronrod(
	Func<double, double> f,
	double intervalBegin,
	double intervalEnd,
	out double error,
	out double L1Norm,
	double targetRelativeError = 1E-08,
	int maximumDepth = 15,
	int order = 15
)

Parameters

f  FuncDouble, Double
The analytic smooth function to integrate.
intervalBegin  Double
Where the interval starts.
intervalEnd  Double
Where the interval stops.
error  Double
The difference between the (N-1)/2 point Gauss approximation and the N-point Gauss-Kronrod approximation
L1Norm  Double
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.
targetRelativeError  Double  (Optional)
The expected relative accuracy of the approximation.
maximumDepth  Int32  (Optional)
The maximum number of interval splittings permitted before stopping
order  Int32  (Optional)
The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points

Return Value

Double
Approximation of the finite integral in the given interval.
See Also