<?xml version="1.0" encoding="UTF-8"?>

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<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="psmall">

    <refnamediv>

        <refname>psmall</refname>

        <refpurpose>スペクトル投影</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A</term>

                <listitem>

                    <para>実数の正方行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>thres</term>

                <listitem>

                    <para>実数</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>flag</term>

                <listitem>

                    <para>

                        文字列 (<literal>'c'</literal> または <literal>'d'</literal>)

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Q,M</term>

                <listitem>

                    <para>実数行列</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            実部 &lt; <literal>thres</literal> (<literal>flag='c'</literal>)

            または絶対値 &lt; <literal>thres</literal>(<literal>flag='d'</literal>)

            となる固有値-部分空間への投影.

        </para>

        <para>

            この投影は<literal>Q*M</literal>により定義されます.

            ここで,

            <literal>Q</literal>は列フルランク,<literal>M</literal>は行フルランク,

            そして<literal>M*Q=eye</literal>です.

        </para>

        <para>

            <literal>flag='c'</literal>の場合,

            <literal>M*A*Q</literal>の固有値 =

            実部&lt; <literal>thres</literal>の<literal>A</literal>の固有値.

        </para>

        <para>

            <literal>flag='d'</literal>の場合,

            <literal>M*A*Q</literal>の固有値 =

            大きさ &lt; <literal>thres</literal>の<literal>A</literal>の固有値.

        </para>

        <para>

            <literal>flag='c'</literal>の場合,

            <literal>[Q1,M1]</literal> = <literal>eye()-Q*M</literal>の

            フルランク分解(<literal>fullrf</literal>)の場合,

            <literal>M1*A*Q1</literal>の固有値 =実部&gt;=

            <literal>thres</literal>の

            <literal>A</literal>の固有値となります.

        </para>

        <para>

            <literal>flag='d'</literal>の場合,

            <literal>[Q1,M1]</literal> =<literal>eye()-Q*M</literal>

            のフルランク分解(<literal>fullrf</literal>)の場合,

            <literal>M1*A*Q1</literal>の固有値 =

            大きさ&gt;=<literal>thres</literal>の

            <literal>A</literal>の固有値.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
[Q,M]=psmall(A,2.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye()-Q*M);
spec(M1*A*Q1)
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="pbig">pbig</link>

            </member>

            <member>

                <link linkend="proj">proj</link>

            </member>

            <member>

                <link linkend="projspec">projspec</link>

            </member>

        </simplelist>

    </refsection>

    <refsection>

        <title>使用される関数</title>

        <para>

            この関数はソートされた Schur形式(scilab

            関数 <literal>schur</literal>)に基づいています.

        </para>

    </refsection>

</refentry>

