<?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="ereduc">

    <refnamediv>

        <refname>ereduc</refname>

        <refpurpose>QZ変換により列階段型行列を計算</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>X</term>

                <listitem>

                    <para>実数エントリを有するm x n 行列.</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>実数の正のスカラー.</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>E</term>

                <listitem>

                    <para>列階段型行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Q</term>

                <listitem>

                    <para>m x m ユニタリ行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Z</term>

                <listitem>

                    <para>n x n ユニタリ行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>stair</term>

                <listitem>

                    <para>添字ベクトル,</para>

                    <variablelist>

                        <varlistentry>

                            <term>*  </term>

                            <listitem>

                                <para>

                                    境界要素<literal>E(i,j)</literal>が端点の場合,

                                    <literal>ISTAIR(i) = + j</literal>.

                                </para>

                            </listitem>

                        </varlistentry>

                        <varlistentry>

                            <term>*  </term>

                            <listitem>

                                <para>

                                    境界要素<literal>E(i,j)</literal>が端点でない場合,

                                    <literal>ISTAIR(i) = - j</literal>.

                                </para>

                            </listitem>

                        </varlistentry>

                    </variablelist>

                    <para>

                        <literal>(i=1,...,M)</literal>

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>rk</term>

                <listitem>

                    <para>整数, 行列のランクの推定値</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>mx n</literal>行列<literal>X</literal> (正則である

            必要はない)を指定すると,

            関数ereducは,列階段型(台形)の

            ユニタリ変換行列<literal>E=Q*X*Z</literal>

            を計算します.

            更に行列<literal>X</literal>のランクが定義されます.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
X=[1 2 3;4 5 6]
[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="fstair">fstair</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

