Error |
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: 4.8.3572.0 (4.8.3572.0)
SyntaxC#
public static Complex Faddeeva( Complex z )
Parameters
- z Complex
- The function argument.
Return Value
ComplexThe faddeeva function w(z).
Remarks
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