scilab/modules/differential_equations/help/en_US/diff.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  13 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="diff" xml:lang="en">
  14     <refnamediv>
  15         <refname>diff</refname>
  16         <refpurpose>Difference and discrete derivative</refpurpose>
  17     </refnamediv>
  18     <refsynopsisdiv>
  19         <title>Calling Sequence</title>
  20         <synopsis>y=diff(x)
  21             y=diff(x [,n [,dim]])
  22         </synopsis>
  23     </refsynopsisdiv>
  24     <refsection>
  25         <title>Arguments</title>
  26         <variablelist>
  27             <varlistentry>
  28                 <term>x</term>
  29                 <listitem>
  30                     <para>vector or matrix (real, complex, sparse or polynomial)</para>
  31                 </listitem>
  32             </varlistentry>
  33             <varlistentry>
  34                 <term>n</term>
  35                 <listitem>
  36                     <para>integer the order of differentiation</para>
  37                 </listitem>
  38             </varlistentry>
  39             <varlistentry>
  40                 <term>dim</term>
  41                 <listitem>
  42                     <para>integer or character string with values "r","c" and "*"</para>
  43                 </listitem>
  44             </varlistentry>
  45             <varlistentry>
  46                 <term>y</term>
  47                 <listitem>
  48                     <para>scalar or vector/matrix</para>
  49                 </listitem>
  50             </varlistentry>
  51         </variablelist>
  52     </refsection>
  53     <refsection>
  54         <title>Description</title>
  55         <para>
  56             <literal>y=diff(x)</literal> compute the difference function
  57             <literal>y=x(2:$)-x(1:$-1)</literal>
  58         </para>
  59         <para>
  60             <literal>diff(x,n,dim)</literal> is the <literal>n</literal>th
  61             difference function along dimension <literal>dim</literal>.
  62         </para>
  63         <para>
  64             <literal>diff(x,n,"*")</literal> is equivalent to
  65             <literal>diff(x(:),n)</literal>.
  66         </para>
  67         <para>
  68             Default value for <literal>n</literal> is 1. Default value for
  69             <literal>dim</literal> is <literal>"*"</literal>.
  70         </para>
  71         <para>
  72             <literal>dim='r'</literal> is equivalent to <literal>dim=1</literal>
  73             and <literal>dim='c'</literal> is equivalent to
  74             <literal>dim=2</literal>.
  75         </para>
  76     </refsection>
  77     <refsection>
  78         <title>Examples</title>
  79         <programlisting role="example"><![CDATA[
  80 v=(1:8)^3;
  81 diff(v)
  82 diff(v,3)
  83
  84 A=[(1:8)^2
  85    (1:8)^3
  86    (1:8)^4];
  87
  88 diff(A,3,2)
  89
  90 //approximate differentiation
  91 step=0.001
  92 t=0:step:10;
  93 y=sin(t);
  94 dy=diff(sin(t))/step; //approximate differentiation of sine function
  95 norm(dy-cos(t(1:$-1)),%inf)
  96  ]]></programlisting>
  97     </refsection>
  98 </refentry>