* Bug 16145 fixed: intg() integrate() intc() default atol
[scilab.git] / scilab / modules / differential_equations / help / en_US / intc.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <!--
3  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
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12  * and continues to be available under such terms.
13  * For more information, see the COPYING file which you should have received
14  * along with this program.
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16  -->
17 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
18           xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML"
19           xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
20           xml:lang="en" xml:id="intc">
21     <refnamediv>
22         <refname>intc</refname>
23         <refpurpose>integral along a straight path in the complex plan</refpurpose>
24     </refnamediv>
25     <refsynopsisdiv>
26         <title>Syntax</title>
27         <synopsis>
28           [y, err] = intc(a, b, f)
29           [y, err] = intc(a, b, f, abserr)
30           [y, err] = intc(a, b, f, abserr, relerr)
31         </synopsis>
32     </refsynopsisdiv>
33     <refsection>
34         <title>Arguments</title>
35         <variablelist>
36             <varlistentry>
37                 <term>a, b</term>
38                 <listitem>
39                       two complex numbers: starting and ending points of the integral in the
40                       complex plan.
41                     <para/>
42                 </listitem>
43             </varlistentry>
44             <varlistentry>
45                 <term>f</term>
46                 <listitem>
47                     Identifier of the function to be integrated.
48                     <para/>
49                 </listitem>
50             </varlistentry>
51             <varlistentry>
52                 <term>abserr, relerr</term>
53                 <listitem>
54                     real scalars: absolute and relative errors.
55                     Default values: <literal>1.d-13</literal> and <literal>1d-8</literal>.
56                     <para/>
57                 </listitem>
58             </varlistentry>
59             <varlistentry>
60                 <term>err</term>
61                 <listitem>
62                     real number: estimated absolute error on the result.
63                     <para/>
64                 </listitem>
65             </varlistentry>
66         </variablelist>
67     </refsection>
68     <refsection>
69         <title>Description</title>
70         <para>
71             If <literal>f</literal> is a complex-valued function, <literal>intc(a, b, f)</literal>
72             computes the integral from <literal>a</literal> to <literal>b</literal> of
73             <literal>f(z)dz</literal> along the  straight line <literal>[a b]</literal>
74             of the complex plan.
75         </para>
76     </refsection>
77     <refsection>
78         <title>Examples</title>
79         <programlisting role="example"><![CDATA[
80 function y = f(z)
81   y = z^(3 + %pi * %i);
82 endfunction
83
84 intc(1+%i, 4-%i, f)
85
86 [r, err] = intc(1+%i, 4-%i, f, 1d-10, 1d-6)
87  ]]></programlisting>
88     </refsection>
89     <refsection role="see also">
90         <title>See also</title>
91         <simplelist type="inline">
92             <member>
93                 <link linkend="intg">intg</link>
94             </member>
95             <member>
96                 <link linkend="intl">intl</link>
97             </member>
98         </simplelist>
99     </refsection>
100     <refsection>
101         <title>History</title>
102         <revhistory>
103             <revision>
104                 <revnumber>5.5.0</revnumber>
105                 <revremark>Absolute and relative (input) and absolute (output) errors management added.</revremark>
106             </revision>
107             <revision>
108                 <revnumber>6.1.0</revnumber>
109                 <revremark>
110                     The default abserr value becomes 10<superscript>-13</superscript> instead of
111                     10<superscript>-14</superscript>.
112                 </revremark>
113             </revision>
114         </revhistory>
115     </refsection>
116 </refentry>