<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA - F.D
 *
 * 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="pfss">
    <refnamediv>
        <refname>pfss</refname>
        <refpurpose>部分分数分解</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>
            elts = pfss(Sl)
            elts = pfss(Sl,rmax)
            elts = pfss(Sl,'cord')
            elts = pfss(Sl, rmax,'cord')
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>Sl</term>
                <listitem>
                    <para>
                        A linear dynamical system in state-space, or a transfer
                        function representation (see <link linkend="syslin">syslin</link>),
                        or any rational fraction.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>rmax</term>
                <listitem>
                    <para>
                        A real number controlling the conditioning of block
                        diagonalization (see  <link linkend="bdiag">bdiag</link>).
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>cord</term>
                <listitem>
                    <para>
                        A character string with possible values <literal>'c'</literal>
                        or <literal>'d'</literal>.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>elts</term>
                <listitem>
                    <para>
                        List of linear systems, or list of rationals: the components of the
                        decomposition.
                    </para>
                    <para>
                        If <literal>Sl</literal> is a transfer function or any other rational
                        and has an integer part (degree(Sl.num)>=degree(Sl.den)),
                        <literal>elts(1:$-1)</literal> are rational components
                        and <literal>elts($)</literal> is the integer part (polynomial).
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            線形システム<literal>Sl</literal>(状態空間形式,伝達行列は
            <literal>tf2ss</literal>により自動的に状態空間形式に変換されます)の部分分数分解:
        </para>
        <para>
            <literal>elts</literal> は,
            加算すると<literal>Sl</literal>となる
            線形システムのリストです.
            すなわち <literal>elts=list(S1,S2,S3,...,Sn)</literal> :
        </para>
        <para>
            ただし,<literal>Sl = S1 + S2 +... +Sn</literal>.
        </para>
        <para>
            各 <literal>Si</literal> は
            <literal>S</literal>の<literal>A</literal>行列のブロック対角に基づく
            <literal/>
            Sのいくつかの極を含みます.
        </para>
        <para>
            プロパーでないシステムの場合,<literal>Sl</literal>の多項式部分が
            <literal>elts</literal>の最後のエントリに置かれます.
        </para>
        <para>
            <literal>Sl</literal>が伝達形式で指定された場合, まず状態空間に変換され,
            その後,各サブシステム<literal>Si</literal>が伝達形式に変換されます.
        </para>
        <para>
            A 行列の状態空間形式は,
            関数<literal>bdiag</literal>によりブロック対角形式に変換されます.
            オプションのパラメータ
            <literal>rmax</literal> は<literal>bdiag</literal>に送られます.
            <literal>rmax</literal> はブロック対角化を成立させるために
            大きな数に設定する必要があります.
        </para>
        <para>
            オプションフラグ <literal>cord='c'</literal> が指定された場合,
            <literal>elts</literal>の要素はA行列の固有値の実部
            (<literal>cord='d'</literal>の場合は大きさ)でソートされます.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
    // With a linear system (state-space):
    W = ssrand(1,1,6);
    elts = pfss(W);
    W1 = 0;
    for k = 1:size(elts)
        W1 = W1 + ss2tf(elts(k));
    end
    clean(ss2tf(W) - W1)
    ]]></programlisting>
        <programlisting role="example"><![CDATA[
    // With a rational (transfer function or any other one), without integer part:
    num = 22801+4406.18*%s + 382.37*%s^2 + 21.02*%s^3;
    den = 22952.25 + 4117.77*%s + 490.63*%s^2 + 33.06*%s^3 + %s^4; // degree(den)>degree(num)
    h2 = syslin('c',num/den)
    d = pfss(h2)

    // With a rational with an integer part: degree(num)>=degree(den):
    num = 22801+4406.18*%s + 382.37*%s^2 + 21.02*%s^3 + %s^5;
    h2 = syslin('c',num/den)
    d = pfss(h2)
    typeof(d($)) // last component = integer part = polynomial
    ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="pbig">pbig</link>
            </member>
            <member>
                <link linkend="bdiag">bdiag</link>
            </member>
            <member>
                <link linkend="coffg">coffg</link>
            </member>
            <member>
                <link linkend="dtsi">dtsi</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
