1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
|
<?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 - Complex error, Faddeeva, Dawson, and Voigt functions</title>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<link rev="made" href="mailto:root@localhost" />
</head>
<body style="background-color: white">
<!-- INDEX BEGIN -->
<div name="index">
<p><a name="__index__"></a></p>
<!--
<ul>
<li><a href="#name">NAME</a></li>
<li><a href="#synopsis">SYNOPSIS</a></li>
<li><a href="#description">DESCRIPTION</a></li>
<li><a href="#resources">RESOURCES</a></li>
<li><a href="#references">REFERENCES</a></li>
<li><a href="#bug_reports">BUG REPORTS</a></li>
<li><a href="#authors">AUTHORS</a></li>
<li><a href="#see_also">SEE ALSO</a></li>
<li><a href="#copying">COPYING</a></li>
</ul>
-->
</div>
<!-- INDEX END -->
<link rel="stylesheet" href="../podstyle.css" type="text/css" /><p>
</p>
<hr />
<h1><a name="name">NAME</a></h1>
<p>w_of_z, im_w_of_x - Faddeeva's rescaled complex error function</p>
<p>
</p>
<hr />
<h1><a name="synopsis">SYNOPSIS</a></h1>
<p><strong>#include <cerf.h</strong>></p>
<p><strong>double _Complex w_of_z ( double _Complex z );</strong></p>
<p><strong>double im_w_of_x ( double x );</strong></p>
<p>
</p>
<hr />
<h1><a name="description">DESCRIPTION</a></h1>
<p>Faddeeva's rescaled complex error function w(z), also called the plasma dispersion function.</p>
<p><strong>w_of_z</strong> returns w(z) = exp(-z^2) * erfc(-i*z).</p>
<p><strong>im_w_of_x</strong> returns Im[w(x)].</p>
<p>
</p>
<hr />
<h1><a name="resources">RESOURCES</a></h1>
<p>Project web site: <a href="http://apps.jcns.fz-juelich.de/libcerf">http://apps.jcns.fz-juelich.de/libcerf</a></p>
<p>
</p>
<hr />
<h1><a name="references">REFERENCES</a></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, <a href="http://ab-initio.mit.edu/Faddeeva">http://ab-initio.mit.edu/Faddeeva</a> (accessed January 2013).</p>
<p>
</p>
<hr />
<h1><a name="bug_reports">BUG REPORTS</a></h1>
<p>Please report bugs to the authors.</p>
<p>
</p>
<hr />
<h1><a name="authors">AUTHORS</a></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 <<a href="mailto:j.wuttke@fz-juelich.de">j.wuttke@fz-juelich.de</a>>, Forschungszentrum Juelich,
reorganized the code into a library, and wrote this man page.</p>
<p>
</p>
<hr />
<h1><a name="see_also">SEE ALSO</a></h1>
<p>This function is used within liberfc to compute several other complex error functions:</p>
<p><strong>dawson(3)</strong>, <strong>voigt(3)</strong>, <strong>cerf(3)</strong>, <strong>erfcx(3)</strong>, <strong>erfi(3)</strong>.</p>
<p>
</p>
<hr />
<h1><a name="copying">COPYING</a></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>
|
