* Bug #12795 fixed - Cacsd doc: typo fixes
[scilab.git] / scilab / modules / cacsd / help / en_US / arsimul.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:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="arsimul">
14     <refnamediv>
15         <refname>arsimul</refname>
16         <refpurpose>armax simulation</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>Calling Sequence</title>
20         <synopsis>[z]=arsimul(a,b,d,sig,u,[up,yp,ep])
21             [z]=arsimul(ar,u,[up,yp,ep])
22         </synopsis>
23     </refsynopsisdiv>
24     <refsection>
25         <title>Arguments</title>
26         <variablelist>
27             <varlistentry>
28                 <term>ar</term>
29                 <listitem>
30                     <para>an armax process. See armac.</para>
31                 </listitem>
32             </varlistentry>
33             <varlistentry>
34                 <term>a</term>
35                 <listitem>
36                     <para>
37                         is the matrix  <literal>[Id,a1,...,a_r]</literal>     of dimension (n,(r+1)*n)
38                     </para>
39                 </listitem>
40             </varlistentry>
41             <varlistentry>
42                 <term>b</term>
43                 <listitem>
44                     <para>
45                         is the matrix <literal>[b0,......,b_s]</literal>      of dimension (n,(s+1)*m)
46                     </para>
47                 </listitem>
48             </varlistentry>
49             <varlistentry>
50                 <term>d</term>
51                 <listitem>
52                     <para>
53                         is the matrix <literal>[Id,d_1,......,d_t]</literal>  of dimension (n,(t+1)*n)
54                     </para>
55                 </listitem>
56             </varlistentry>
57             <varlistentry>
58                 <term>u</term>
59                 <listitem>
60                     <para>is a matrix  (m,N), which gives the entry u(:,j)=u_j</para>
61                 </listitem>
62             </varlistentry>
63             <varlistentry>
64                 <term>sig</term>
65                 <listitem>
66                     <para>is a  (n,n) matrix  e_{k} is an n-dimensional Gaussian process with variance I</para>
67                 </listitem>
68             </varlistentry>
69             <varlistentry>
70                 <term>up, yp</term>
71                 <listitem>
72                     <para>
73                         optional parameter which describe the past.  <literal>up=[ u_0,u_{-1},...,u_{s-1}]</literal>;
74                         <literal>yp=[ y_0,y_{-1},...,y_{r-1}];</literal>   <literal>ep=[ e_0,e_{-1},...,e_{r-1}]</literal>;
75                         if they are omitted, the past value are supposed to be zero
76                     </para>
77                 </listitem>
78             </varlistentry>
79             <varlistentry>
80                 <term>z</term>
81                 <listitem>
82                     <para>
83                         <literal>z=[y(1),....,y(N)]</literal>
84                     </para>
85                 </listitem>
86             </varlistentry>
87         </variablelist>
88     </refsection>
89     <refsection>
90         <title>Description</title>
91         <para>
92             simulation of an n-dimensional armax process
93             <literal>A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)</literal>
94         </para>
95         <programlisting role=""><![CDATA[
96 A(z)= Id+a1*z+...+a_r*z^r;  ( r=0  => A(z)=Id)
97 B(z)= b0+b1*z+...+b_s z^s;  ( s=-1 => B(z)=[])
98 D(z)= Id+d1*z+...+d_t z^t;  ( t=0  => D(z)=Id)
99  ]]></programlisting>
100         <para>
101             z et e are in  <literal>R^n</literal> et u in <literal>R^m</literal>
102         </para>
103     </refsection>
104     <refsection>
105         <title>Method</title>
106         <para>
107             a state-space representation is constructed and an ode with the option
108             <literal>"discrete"</literal> is used to compute <literal>z</literal>.
109         </para>
110     </refsection>
111     <refsection>
112         <title>Examples</title>
113         <programlisting role="example"><![CDATA[
114 a=[1,-2.851,2.717,-0.865].*.eye(2,2)
115 b=[0,1,1,1].*.[1;1];
116 d=[1,0.7,0.2].*.eye(2,2);
117 sig=eye(2,2);
118 ar=armac(a,b,d,2,1,sig)
119 u=rand(1,10,'normal');
120 y=arsimul(ar,u)
121  ]]></programlisting>
122     </refsection>
123 </refentry>