<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) ENPC - JPC
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
 *
 -->
<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="ja" xml:id="arsimul">
    <refnamediv>
        <refname>arsimul</refname>
        <refpurpose>armaxシミュレーション</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[z]=arsimul(a,b,d,sig,u,[up,yp,ep])
            [z]=arsimul(ar,u,[up,yp,ep])
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>ar</term>
                <listitem>
                    <para>armaxプロセス. armac参照.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>a</term>
                <listitem>
                    <para>
                        (n,(r+1)*n)次の行列  <literal>[Id,a1,...,a_r]</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>b</term>
                <listitem>
                    <para>
                        (n,(s+1)*m)次の行列 <literal>[b0,......,b_s]</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>d</term>
                <listitem>
                    <para>
                        (n,(t+1)*n)次の行列<literal>[Id,d_1,......,d_t]</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>u</term>
                <listitem>
                    <para>行列(m,N), エントリu(:,j)=u_jを指定</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>sig</term>
                <listitem>
                    <para>(n,n)行列  e_{k} で分散Iのn次ガウス過程</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>up, yp</term>
                <listitem>
                    <para>
                        前の値を記述するオプションのパラメータ.  <literal>up=[ u_0,u_{-1},...,u_{s-1}]</literal>;
                        <literal>yp=[ y_0,y_{-1},...,y_{r-1}];</literal>   <literal>ep=[ e_0,e_{-1},...,e_{r-1}]</literal>;
                        省略された場合, 前の値はゼロであると仮定されます.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>z</term>
                <listitem>
                    <para>
                        <literal>z=[y(1),....,y(N)]</literal>
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            以下のn次元 armax プロセスのシミュレーションを行います,
            <literal>A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)</literal>
        </para>
        <programlisting role=""><![CDATA[
A(z)= Id+a1*z+...+a_r*z^r;  ( r=0  => A(z)=Id)
B(z)= b0+b1*z+...+b_s z^s;  ( s=-1 => B(z)=[])
D(z)= Id+d1*z+...+d_t z^t;  ( t=0  => D(z)=Id)
 ]]></programlisting>
        <para>
            ただし,
            z と e は <literal>R^n</literal>,  u は <literal>R^m</literal>です.
        </para>
    </refsection>
    <refsection>
        <title>手法</title>
        <para>
            状態空間表現が構築され,
            odeにオプション "discrete"を指定することにより,
            zを計算することができます.
        </para>
    </refsection>
</refentry>
