wofz.cpp File Reference

Implements a function to calculate the Faddeeva function \( W(z) \). More...

Functions
std::complex< double >	ITS::Propagation::LFMF::wofz (const std::complex< double > z)
	This function computes the Faddeeva function \( W(z) = e^{-z^2} \mathrm{erfc}(-iz) \).

Detailed Description

Implements a function to calculate the Faddeeva function \( W(z) \).

Function Documentation

wofz()

std::complex< double > ITS::Propagation::LFMF::wofz

(

const std::complex< double >

z

)

This function computes the Faddeeva function \( W(z) = e^{-z^2} \mathrm{erfc}(-iz) \).

Given a complex input argument \( z \), this function computes the value of the above equation, in which \(\mathrm{erfc}\) is the complex complementary error function and \( i \) is \( \sqrt{-1} \).

The basis for this function is Algorithm 680, Collected Algorithms from ACM, (reference provided below). This version of the function accepts a single complex input argument z and returns a single complex output. The following note is restated from the original implementation's description:

Note

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.

Parameters

[in]

z

Input argument

Returns

The desired \( W(z) \) function calculated at z

Lineage

• The original FORTRAN implementation was translated to C/C++ by I. Stevanovic (OFCOM CH).
• Direct comparisons of double values with == were removed by C. Heroy, who implemented AlmostEqualRelative().

References

• Algorithm 680, Collected Algorithms from ACM, Transactions of Mathematical Software, Vol. 16, No. 1, pp. 47: https://doi.org/10.1145/77626.77630