ComplexErrorFunctionRelated Class

Contains functions that are related to the complex error function of complex argument.

Inheritance Hierarchy

SystemObject
Altaxo.CalcComplexErrorFunctionRelated

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)

Syntax

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public class ComplexErrorFunctionRelated

The ComplexErrorFunctionRelated type exposes the following members.

Constructors

	Name	Description
	ComplexErrorFunctionRelated	Initializes a new instance of the ComplexErrorFunctionRelated class

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Methods

	Name	Description
	CDawson	Dawson's integral D(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z).
	Cerf	Complex error function.
	Cerfc	The complex complementary error function cerfc(z) = 1 - cerf(z).
	Cerfcx	The underflow-compensating function cerfcx(z) = exp(z^2)*cerfc(z).
	Cerfi	The imaginary error function cerfi(z) = -i cerf(iz).
	Dawson	Dawson's integral D(x) = sqrt(pi)/2 * exp(-x^2) * erfi(x) for real values.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Erfcx	The underflow-compensating function erfcx(x) = exp(x^2)*erfc(x) for real arguments.
	Erfi	The imaginary error function erfi(x) = -i cerf(ix).
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	Im_w_of_z	Faddeeva's scaled complex error function w(z) = exp(-z^2) erfc(-iz), returning the purely imaginary result as a real number.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	Re_w_of_z	Faddeeva's scaled complex error function w(z) = exp(-z^2) erfc(-iz), returning the real part of the result as a real number.
	ToString	Returns a string that represents the current object. (Inherited from Object)
	Voigt	The convolution of a Gaussian and a Lorentzian probability density function.
	VoigtHalfWidthHalfMaximum	The half width at half maximum of the Voigt(Double, Double, Double) profile.
	VoigtHalfWidthHalfMaximumApproximation	An approximation formula for the half width at half maximum of the Voigt(Double, Double, Double) profile. The maximal relative error is 0.0216%. The error is vanishing in the limiting cases sigma>>gamma and gamma>>sigma.
	W_of_z	Faddeeva's scaled complex error function w(z) = exp(-z^2) erfc(-iz).

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Fields

	Name	Description
	VoigtHalfWidthHalfMaximumApproximationMaximalRelativeError	Gets the maximal relative error of the VoigtHalfWidthHalfMaximumApproximation(Double, Double).

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Remarks

Citation:

S. G. Johnson, J. Wuttke: libcerf, numeric library for complex error functions, see https://jugit.fz-juelich.de/mlz/libcerf.

Most function evaluations in this library rely on Faddeeva's function w(z). This function has been reimplemented from scratch by Steven G.Johnson; project web site http://ab-initio.mit.edu/Faddeeva. The implementation partly relies on algorithms from the following publications:

References:

Walter Gautschi, Efficient computation of the complex error function, SIAM J. Numer. Anal. 7, 187 (1970).

G. P. M. Poppe and C. M. J. Wijers, More efficient computation of the complex error function, ACM Trans. Math. Soft. 16, 38 (1990).

Mofreh R. Zaghloul and Ahmed N. Ali, Algorithm 916: Computing the Faddeyeva and Voigt Functions, ACM Trans. Math. Soft. 38, 15 (2011).

Reference

Altaxo.Calc Namespace