File: Numerical-Differentiation-Examples.html

package info (click to toggle)
gsl-ref-html 1.16-1
  • links: PTS
  • area: non-free
  • in suites: jessie, jessie-kfreebsd, stretch
  • size: 5,816 kB
  • ctags: 4,130
  • sloc: makefile: 35
file content (126 lines) | stat: -rw-r--r-- 4,994 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
 
<!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 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 no
Invariant Sections and no cover texts.  A copy of the license is
included in the section entitled "GNU Free Documentation License". -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: Numerical Differentiation Examples</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Numerical Differentiation Examples">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Numerical Differentiation 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="Numerical-Differentiation.html#Numerical-Differentiation" rel="up" title="Numerical Differentiation">
<link href="Numerical-Differentiation-References.html#Numerical-Differentiation-References" rel="next" title="Numerical Differentiation References">
<link href="Numerical-Differentiation-functions.html#Numerical-Differentiation-functions" rel="previous" title="Numerical Differentiation functions">
<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="Numerical-Differentiation-Examples"></a>
<div class="header">
<p>
Next: <a href="Numerical-Differentiation-References.html#Numerical-Differentiation-References" accesskey="n" rel="next">Numerical Differentiation References</a>, Previous: <a href="Numerical-Differentiation-functions.html#Numerical-Differentiation-functions" accesskey="p" rel="previous">Numerical Differentiation functions</a>, Up: <a href="Numerical-Differentiation.html#Numerical-Differentiation" accesskey="u" rel="up">Numerical Differentiation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Examples-20"></a>
<h3 class="section">28.2 Examples</h3>

<p>The following code estimates the derivative of the function 
<em>f(x) = x^{3/2}</em> 
at <em>x=2</em> and at <em>x=0</em>.  The function <em>f(x)</em> is
undefined for <em>x&lt;0</em> so the derivative at <em>x=0</em> is computed
using <code>gsl_deriv_forward</code>.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_math.h&gt;
#include &lt;gsl/gsl_deriv.h&gt;

double f (double x, void * params)
{
  return pow (x, 1.5);
}

int
main (void)
{
  gsl_function F;
  double result, abserr;

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

  printf (&quot;f(x) = x^(3/2)\n&quot;);

  gsl_deriv_central (&amp;F, 2.0, 1e-8, &amp;result, &amp;abserr);
  printf (&quot;x = 2.0\n&quot;);
  printf (&quot;f'(x) = %.10f +/- %.10f\n&quot;, result, abserr);
  printf (&quot;exact = %.10f\n\n&quot;, 1.5 * sqrt(2.0));

  gsl_deriv_forward (&amp;F, 0.0, 1e-8, &amp;result, &amp;abserr);
  printf (&quot;x = 0.0\n&quot;);
  printf (&quot;f'(x) = %.10f +/- %.10f\n&quot;, result, abserr);
  printf (&quot;exact = %.10f\n&quot;, 0.0);

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

<p>Here is the output of the program,
</p>
<div class="example">
<pre class="example">$ ./a.out
</pre><pre class="verbatim">f(x) = x^(3/2)
x = 2.0
f'(x) = 2.1213203120 +/- 0.0000004064
exact = 2.1213203436

x = 0.0
f'(x) = 0.0000000160 +/- 0.0000000339
exact = 0.0000000000
</pre></div>




</body>
</html>