<?xml version="1.0" ?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>libcerf\ manual</title> <meta http-equiv="content-type" content="text/html; charset=utf-8" /> <link rev="made" href="mailto:root@localhost" /> </head> <body> <link rel="stylesheet" href="podstyle.css" type="text/css" /> <h1 id="NAME">NAME</h1> <p>w_of_z, im_w_of_x - Faddeeva's rescaled complex error function</p> <h1 id="SYNOPSIS">SYNOPSIS</h1> <p><b>#include <cerf.h</b>></p> <p><b>double _Complex w_of_z ( double _Complex z );</b></p> <p><b>double im_w_of_x ( double x );</b></p> <h1 id="DESCRIPTION">DESCRIPTION</h1> <p>Faddeeva's rescaled complex error function w(z), also called the plasma dispersion function.</p> <p><b>w_of_z</b> returns w(z) = exp(-z^2) * erfc(-i*z).</p> <p><b>im_w_of_x</b> returns Im[w(x)].</p> <h1 id="REFERENCES">REFERENCES</h1> <p>To compute w(z), a combination of two algorithms is used:</p> <p>For sufficiently large |z|, a continued-fraction expansion similar to those described by Gautschi (1970) and Poppe & Wijers (1990).</p> <p>Otherwise, Algorithm 916 by Zaghloul & Ali (2011), which is generally competitive at small |z|, and more accurate than the Poppe & Wijers expansion in some regions, e.g. in the vicinity of z=1+i.</p> <p>To compute Im[w(x)], Chebyshev polynomials and continous fractions are used.</p> <p>Milton Abramowitz and Irene M. Stegun, "Handbook of Mathematical Functions", National Bureau of Standards (1964): Formula (7.1.3) introduces the nameless function w(z).</p> <p>Walter Gautschi, "Efficient computation of the complex error function," SIAM J. Numer. Anal. 7, 187 (1970).</p> <p>G. P. M. Poppe and C. M. J. Wijers, "More efficient computation of the complex error function," ACM Trans. Math. Soft. 16, 38 (1990).</p> <p>Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38, 15 (2011).</p> <p>Steven G. Johnson, http://ab-initio.mit.edu/Faddeeva</p> <h1 id="SEE-ALSO">SEE ALSO</h1> <p>This function is used to compute several other complex error functions: <b>dawson(3)</b>, <b>voigt(3)</b>, <b>cerf(3)</b>, <b>erfcx(3)</b>, <b>erfi(3)</b>.</p> <p>Homepage: http://apps.jcns.fz-juelich.de/libcerf</p> <h1 id="AUTHORS">AUTHORS</h1> <p>Steven G. Johnson, http://math.mit.edu/~stevenj, Massachusetts Institute of Technology, researched the numerics, and implemented the Faddeeva function.</p> <p>Joachim Wuttke <j.wuttke@fz-juelich.de>, Forschungszentrum Juelich, reorganized the code into a library, and wrote this man page.</p> <p>Please report bugs to the authors.</p> <h1 id="COPYING">COPYING</h1> <p>Copyright (c) 2012 Massachusetts Institute of Technology</p> <p>Copyright (c) 2013 Forschungszentrum Juelich GmbH</p> <p>Software: MIT License.</p> <p>This documentation: Creative Commons Attribution Share Alike.</p> </body> </html>
distrib
>
Mageia
>
7
>
armv7hl
>
media
>
core-release
>
by-pkgid
>
19dbfa263dc44046d331b3834e323937
>
files
>
14
