japanese translation updated for linear-algebra.
[scilab.git] / scilab / modules / linear_algebra / help / ja_JP / linear / aff2ab.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2
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14
15 <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="aff2ab">
16     
17     <refnamediv>
18         
19         <refname>aff2ab</refname>
20         
21         <refpurpose>線形 (アフィン)関数を A,b に変換</refpurpose>
22         
23     </refnamediv>
24     
25     <refsynopsisdiv>
26         
27         <title>呼び出し手順</title>
28         
29         <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis>
30         
31     </refsynopsisdiv>
32     
33     <refsection>
34         
35         <title>引数</title>
36         
37         <variablelist>
38             
39             <varlistentry>
40                 
41                 <term>afunction</term>
42                 
43                 <listitem>
44                     
45                     <para>
46                         
47                         scilab 関数 <literal> Y =fct(X,D) </literal> 
48                         
49                         ただし, <literal>X, D, Y</literal> は行列の<literal>リスト</literal>
50                         
51                     </para>
52                     
53                 </listitem>
54                 
55             </varlistentry>
56             
57             <varlistentry>
58                 
59                 <term>dimX</term>
60                 
61                 <listitem>
62                     
63                     <para>
64                         
65                         p x 2 整数行列 (<literal>p</literal> は
66                         
67                         <literal>X</literal>の行列の数)
68                         
69                     </para>
70                     
71                 </listitem>
72                 
73             </varlistentry>
74             
75             <varlistentry>
76                 
77                 <term>D</term>
78                 
79                 <listitem>
80                     
81                     <para>
82                         
83                         実数行列の<literal>list</literal>  (または任意の有効なScilab オブジェクト).
84                         
85                     </para>
86                     
87                 </listitem>
88                 
89             </varlistentry>
90             
91             <varlistentry>
92                 
93                 <term>flag</term>
94                 
95                 <listitem>
96                     
97                     <para>
98                         
99                         オプションのパラメータ (<literal>flag='f'</literal> 
100                         
101                         または <literal>flag='sp'</literal>)
102                         
103                     </para>
104                     
105                 </listitem>
106                 
107             </varlistentry>
108             
109             <varlistentry>
110                 
111                 <term>A</term>
112                 
113                 <listitem>
114                     
115                     <para>実数行列</para>
116                     
117                 </listitem>
118                 
119             </varlistentry>
120             
121             <varlistentry>
122                 
123                 <term>b</term>
124                 
125                 <listitem>
126                     
127                     <para>
128                         
129                         <literal>A</literal>と同じ行次元を有する実数ベクトル
130                         
131                     </para>
132                     
133                 </listitem>
134                 
135             </varlistentry>
136             
137         </variablelist>
138         
139     </refsection>
140     
141     <refsection>
142         
143         <title>説明</title>
144         
145         <para>
146             
147             <literal>aff2ab</literal>は,アフィン関数の(正準形式の)行列表現を返します.
148             
149         </para>
150         
151         <para>
152             
153             <literal>afunction</literal> は以下の規定の構文を有する関数です:
154             
155             <literal> Y=afunction(X,D) </literal> 
156             
157             ただし, <literal> X=list(X1,X2,...,Xp) </literal> は
158             
159             p 個の実数行列のリスト,<literal> Y=list(Y1,...,Yq) </literal> は
160             
161             <literal> Xi</literal>に線形に依存するq 個の実数行列のリストです.
162             
163             (オプションの) 入力 <literal> D</literal> は, X の関数として
164             
165             Yを計算するために必要なパラメータを有しています.
166             
167         </para>
168         
169         <para>
170             
171             <literal> dimX</literal> は p x 2 行列です: <literal>dimX(i)=[nri,nci]</literal>
172             
173             は行列<literal>Xi</literal>の行と列の実際の数です.
174             
175             これらの次元は,結果の行列<literal>A</literal>の列の次元である
176             
177             <literal>na</literal> を以下のように定義します:
178             
179             <literal>na=nr1*nc1 +...+ nrp*ncp</literal>.
180             
181         </para>
182         
183         <para>
184             
185             オプションのパラメータ <literal>flag='sp'</literal> が指定された場合,
186             
187             結果の行列 <literal>A</literal>は疎行列として返されます.
188             
189         </para>
190         
191         <para>
192             
193             この関数は,未知変数が行列であるような
194             
195             線形方程式のシステムを解くために有用です.
196             
197         </para>
198         
199     </refsection>
200     
201     <refsection>
202         
203         <title>例</title>
204         
205         <programlisting role="example"><![CDATA[ 
206 // リアプノフ方程式ソルバ (未知変数1つ, 拘束条件1つ)
207 deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)')
208 A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3];
209 [Aly,bly]=aff2ab(lyapunov,dimX,D);
210 [Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); lyapunov(Xv,D)
211 Xm=Xv(:); A'*Xm+Xm*A-Q
212 // 冗長な拘束 t X=X'を有するリアプノフ方程式ソルバ
213 // (変数1つ, 拘束条件2つt) D はグローバル変数
214 deff('Y=ly2(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q,Xm''-Xm)')
215 A=rand(3,3);Q=rand(3,3);Q=Q+Q';D=list(A,Q);dimX=[3,3];
216 [Aly,bly]=aff2ab(ly2,dimX,D);
217 [Xl,kerA]=linsolve(Aly,bly); Xv=vec2list(Xl,dimX); ly2(Xv,D)
218 // フランシス方程式
219 // 以下のような行列 X1 および X2 を見つける:
220 // A1*X1 - X1*A2 + B*X2 -A3 = 0
221 // D1*X1 -D2 = 0 
222 deff('Y=bruce(X,D)','[A1,A2,A3,B,D1,D2]=D(:),...
223 [X1,X2]=X(:);Y=list(A1*X1-X1*A2+B*X2-A3,D1*X1-D2)')
224 A1=[-4,10;-1,2];A3=[1;2];B=[0;1];A2=1;D1=[0,1];D2=1;
225 D=list(A1,A2,A3,B,D1,D2);
226 [n1,m1]=size(A1);[n2,m2]=size(A2);[n3,m3]=size(B);
227 dimX=[[m1,n2];[m3,m2]];
228 [Af,bf]=aff2ab(bruce,dimX,D);
229 [Xf,KerAf]=linsolve(Af,bf);Xsol=vec2list(Xf,dimX)
230 bruce(Xsol,D)
231 // Aを変換する全てのXを見つける
232 deff('y=f(X,D)','y=list(D(:)*X(:)-X(:)*D(:))')
233 A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A));
234 [Xf,KerAf]=linsolve(Af,bf);[p,q]=size(KerAf);
235 Xsol=vec2list(Xf+KerAf*rand(q,1),dimX);
236 C=Xsol(:); A*C-C*A
237  ]]></programlisting>
238         
239     </refsection>
240     
241     <refsection role="see also">
242         
243         <title>参照</title>
244         
245         <simplelist type="inline">
246             
247             <member>
248                 
249                 <link linkend="linsolve">linsolve</link>
250                 
251             </member>
252             
253         </simplelist>
254         
255     </refsection>
256     
257 </refentry>
258