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ErrorFunctionFaddeeva(Complex, Boolean) Method

Given a complex number z = (x,y), this subroutine computes the value of the Faddeeva function w(z) = exp(-z^2)*erfc(-i*z), where erfc is the complex complementary error function and i means sqrt(-1).

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public static Complex Faddeeva(
	Complex z,
	bool bDebug
)

Parameters

z  Complex
The function argument.
bDebug  Boolean
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.

Return Value

Complex
The faddeeva function w(z).
Remarks
C#
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The accuracy of the algorithm for z in the 1st and 2nd quadrant
is 14 significant digits; in the 3rd and 4th it is 13 significant
digits outside a circular region with radius 0.126 around a zero
of the function.

All real variables in the program are double precision.
The parameter M_2_SQRTPI equals 2/sqrt(pi).

The routine is not underflow-protected but any variable can be
put to 0 upon underflow;

The routine is overflow-protected: Matpack::Error() is called.

References:

(1) G.P.M. Poppe, C.M.J. Wijers; More Efficient Computation of
    the Complex64T Error-Function, ACM Trans. Math. Software,
    Vol. 16, no. 1, pp. 47.
(2) Algorithm 680, collected algorithms from ACM.

The Fortran source code was translated to C++ by B.M. Gammel
and added to the Matpack library, 1992.

Last change: B. M. Gammel, 18.03.1996 error handling
See Also