<?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="linsolve">
    <refnamediv>
        <refname>linsolve</refname>
        <refpurpose>線形方程式ソルバ</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>引数</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>
                        a <literal>na x ma</literal> 実数行列 (疎行列の場合もあり)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>b</term>
                <listitem>
                    <para>
                        <literal>na x 1</literal>ベクトル (<literal>A</literal>の行と同じ次元)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>x0</term>
                <listitem>
                    <para>実数ベクトル</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>kerA</term>
                <listitem>
                    <para>
                        <literal>ma x k</literal> 実数行列
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            <literal>linsolve</literal>  は,
            <literal> A*x+b=0</literal>の解を全て計算します.
        </para>
        <para>
            <literal>x0</literal> は特解 (存在する場合),
            <literal> kerA </literal> は<literal>A</literal>のヌル空間です.
            任意の<literal>w</literal>について<literal>x=x0+kerA*w</literal>は,
            <literal> A*x+b=0</literal>を満たします.
        </para>
        <para>
            互換性のある <literal>x0</literal> がエントリに指定された場合,
            <literal>x0</literal>が返されます.
            そうでない場合,<literal>x0</literal>と互換性のあるもの(存在する場合)が返されます.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
A=rand(5,3)*rand(3,8);
b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique

// Benchmark with other linear sparse solver:
[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/demos/bcsstk24.rsa");
b = zeros(size(A,1),1);

tic();
res = umfpack(A,'\',b);
mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());

tic();
res = linsolve(A,b);
mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());

tic();
res = A\b;
mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="inv">inv</link>
            </member>
            <member>
                <link linkend="pinv">pinv</link>
            </member>
            <member>
                <link linkend="colcomp">colcomp</link>
            </member>
            <member>
                <link linkend="im_inv">im_inv</link>
            </member>
            <member>
                <link linkend="umfpack">umfpack</link>
            </member>
            <member>
                <link linkend="backslash">backslash</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
