aff2ab.xml updated
[scilab.git] / scilab / modules / linear_algebra / help / ja_JP / linear / linsolve.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2
3 <!--
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14  * along with this program.
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17
18 <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">
19
20     <refnamediv>
21
22         <refname>linsolve</refname>
23
24         <refpurpose>線形方程式ソルバ</refpurpose>
25
26     </refnamediv>
27
28     <refsynopsisdiv>
29
30         <title>呼び出し手順</title>
31
32         <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
33
34     </refsynopsisdiv>
35
36     <refsection>
37
38         <title>引数</title>
39
40         <variablelist>
41
42             <varlistentry>
43
44                 <term>A</term>
45
46                 <listitem>
47
48                     <para>
49
50                         a <literal>na x ma</literal> 実数行列 (疎行列の場合もあり)
51
52                     </para>
53
54                 </listitem>
55
56             </varlistentry>
57
58             <varlistentry>
59
60                 <term>b</term>
61
62                 <listitem>
63
64                     <para>
65
66                         <literal>na x 1</literal>ベクトル (<literal>A</literal>の行と同じ次元)
67
68                     </para>
69
70                 </listitem>
71
72             </varlistentry>
73
74             <varlistentry>
75
76                 <term>x0</term>
77
78                 <listitem>
79
80                     <para>実数ベクトル</para>
81
82                 </listitem>
83
84             </varlistentry>
85
86             <varlistentry>
87
88                 <term>kerA</term>
89
90                 <listitem>
91
92                     <para>
93
94                         <literal>ma x k</literal> 実数行列
95
96                     </para>
97
98                 </listitem>
99
100             </varlistentry>
101
102         </variablelist>
103
104     </refsection>
105
106     <refsection>
107
108         <title>説明</title>
109
110         <para>
111
112             <literal>linsolve</literal>  は,
113
114             <literal> A*x+b=0</literal>の解を全て計算します.
115
116         </para>
117
118         <para>
119
120             <literal>x0</literal> は特解 (存在する場合),
121
122             <literal> kerA </literal> は<literal>A</literal>のヌル空間です.
123
124             任意の<literal>w</literal>について<literal>x=x0+kerA*w</literal>は,
125
126             <literal> A*x+b=0</literal>を満たします.
127
128         </para>
129
130         <para>
131
132             互換性のある <literal>x0</literal> がエントリに指定された場合,
133
134             <literal>x0</literal>が返されます.
135
136             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.
137
138         </para>
139
140     </refsection>
141
142     <refsection>
143
144         <title>例</title>
145
146         <programlisting role="example"><![CDATA[
147 A=rand(5,3)*rand(3,8);
148 b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
149 b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
150 A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique
151 // Benchmark with other linear sparse solver:
152 [A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa");
153 b = zeros(size(A,1),1);
154 tic();
155 res = umfpack(A,'\',b);
156 mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
157 tic();
158 res = linsolve(A,b);
159 mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
160 tic();
161 res = A\b;
162 mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
163  ]]></programlisting>
164
165     </refsection>
166
167     <refsection role="see also">
168
169         <title>参照</title>
170
171         <simplelist type="inline">
172
173             <member>
174
175                 <link linkend="inv">inv</link>
176
177             </member>
178
179             <member>
180
181                 <link linkend="pinv">pinv</link>
182
183             </member>
184
185             <member>
186
187                 <link linkend="colcomp">colcomp</link>
188
189             </member>
190
191             <member>
192
193                 <link linkend="im_inv">im_inv</link>
194
195             </member>
196
197             <member>
198
199                 <link linkend="umfpack">umfpack</link>
200
201             </member>
202
203             <member>
204
205                 <link linkend="backslash">backslash</link>
206
207             </member>
208
209         </simplelist>
210
211     </refsection>
212
213 </refentry>
214