File: Chebyshev-Approximation-Examples.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (134 lines) | stat: -rw-r--r-- 5,213 bytes parent folder | download
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
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".

(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: Chebyshev Approximation Examples</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Chebyshev Approximation Examples">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Chebyshev Approximation Examples">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Chebyshev-Approximations.html#Chebyshev-Approximations" rel="up" title="Chebyshev Approximations">
<link href="Chebyshev-Approximation-References-and-Further-Reading.html#Chebyshev-Approximation-References-and-Further-Reading" rel="next" title="Chebyshev Approximation References and Further Reading">
<link href="Derivatives-and-Integrals.html#Derivatives-and-Integrals" rel="previous" title="Derivatives and Integrals">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Chebyshev-Approximation-Examples"></a>
<div class="header">
<p>
Next: <a href="Chebyshev-Approximation-References-and-Further-Reading.html#Chebyshev-Approximation-References-and-Further-Reading" accesskey="n" rel="next">Chebyshev Approximation References and Further Reading</a>, Previous: <a href="Derivatives-and-Integrals.html#Derivatives-and-Integrals" accesskey="p" rel="previous">Derivatives and Integrals</a>, Up: <a href="Chebyshev-Approximations.html#Chebyshev-Approximations" accesskey="u" rel="up">Chebyshev Approximations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Examples-21"></a>
<h3 class="section">30.6 Examples</h3>

<p>The following example program computes Chebyshev approximations to a
step function.  This is an extremely difficult approximation to make,
due to the discontinuity, and was chosen as an example where
approximation error is visible.  For smooth functions the Chebyshev
approximation converges extremely rapidly and errors would not be
visible.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_math.h&gt;
#include &lt;gsl/gsl_chebyshev.h&gt;

double
f (double x, void *p)
{
  (void)(p); /* avoid unused parameter warning */

  if (x &lt; 0.5)
    return 0.25;
  else
    return 0.75;
}

int
main (void)
{
  int i, n = 10000; 

  gsl_cheb_series *cs = gsl_cheb_alloc (40);

  gsl_function F;

  F.function = f;
  F.params = 0;

  gsl_cheb_init (cs, &amp;F, 0.0, 1.0);

  for (i = 0; i &lt; n; i++)
    {
      double x = i / (double)n;
      double r10 = gsl_cheb_eval_n (cs, 10, x);
      double r40 = gsl_cheb_eval (cs, x);
      printf (&quot;%g %g %g %g\n&quot;, 
              x, GSL_FN_EVAL (&amp;F, x), r10, r40);
    }

  gsl_cheb_free (cs);

  return 0;
}
</pre></div>

<p>The output from the program gives the original function, 10-th order
approximation and 40-th order approximation, all sampled at intervals of
0.001 in <em>x</em>.
</p>




</body>
</html>