%s*eye()-A where A is a matrix of doubles produces an error. So eye() is replaced...
[scilab.git] / scilab / modules / linear_algebra / help / ja_JP / eigen / spec.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2
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11  * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
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13  -->
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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="spec" xml:lang="ja">
16     
17     <refnamediv>
18         
19         <refname>spec</refname>
20         
21         <refpurpose>行列とペンシルの固有値</refpurpose>
22         
23     </refnamediv>
24     
25     <refsynopsisdiv>
26         
27         <title>呼び出し手順</title>
28         
29         <synopsis>evals=spec(A)
30             
31             [R,diagevals]=spec(A)
32             
33             
34             
35             evals=spec(A,B)
36             
37             [alpha,beta]=spec(A,B)
38             
39             [alpha,beta,Z]=spec(A,B)
40             
41             [alpha,beta,Q,Z]=spec(A,B)
42             
43         </synopsis>
44         
45     </refsynopsisdiv>
46     
47     <refsection>
48         
49         <title>引数</title>
50         
51         <variablelist>
52             
53             <varlistentry>
54                 
55                 <term>A</term>
56                 
57                 <listitem>
58                     
59                     <para>実数または複素正方行列</para>
60                     
61                 </listitem>
62                 
63             </varlistentry>
64             
65             <varlistentry>
66                 
67                 <term>B</term>
68                 
69                 <listitem>
70                     
71                     <para>
72                         
73                         <literal> A</literal>と同じ次元の実数または複素正方行列
74                         
75                     </para>
76                     
77                 </listitem>
78                 
79             </varlistentry>
80             
81             <varlistentry>
82                 
83                 <term>evals</term>
84                 
85                 <listitem>
86                     
87                     <para>実数または複素ベクトル, 固有値</para>
88                     
89                 </listitem>
90                 
91             </varlistentry>
92             
93             <varlistentry>
94                 
95                 <term>diagevals</term>
96                 
97                 <listitem>
98                     
99                     <para>実数または(対角項に固有値を有する)複素対角行列 </para>
100                     
101                 </listitem>
102                 
103             </varlistentry>
104             
105             <varlistentry>
106                 
107                 <term>alpha</term>
108                 
109                 <listitem>
110                     
111                     <para>実数または複素ベクトル, al./be により固有値が得られます</para>
112                     
113                 </listitem>
114                 
115             </varlistentry>
116             
117             <varlistentry>
118                 
119                 <term>beta</term>
120                 
121                 <listitem>
122                     
123                     <para>実数ベクトル, al./be により固有値が得られます</para>
124                     
125                 </listitem>
126                 
127             </varlistentry>
128             
129             <varlistentry>
130                 
131                 <term>R</term>
132                 
133                 <listitem>
134                     
135                     <para>可逆な実数または複素正方行列, 行列右固有ベクトル.</para>
136                     
137                 </listitem>
138                 
139             </varlistentry>
140             
141             <varlistentry>
142                 
143                 <term>L</term>
144                 
145                 <listitem>
146                     
147                     <para>可逆な実数または複素正方行列, ペンシル左固有ベクトル.</para>
148                     
149                 </listitem>
150                 
151             </varlistentry>
152             
153             <varlistentry>
154                 
155                 <term>R</term>
156                 
157                 <listitem>
158                     
159                     <para>可逆な実数または複素正方行列, ペンシル右固有ベクトル.</para>
160                     
161                 </listitem>
162                 
163             </varlistentry>
164             
165         </variablelist>
166         
167     </refsection>
168     
169     <refsection>
170         
171         <title>説明</title>
172         
173         <variablelist>
174             
175             <varlistentry>
176                 
177                 <term>evals=spec(A)</term>
178                 
179                 <listitem>
180                     
181                     <para>
182                         
183                         ベクトル<literal>evals</literal> に固有値を返します.
184                         
185                     </para>
186                     
187                 </listitem>
188                 
189             </varlistentry>
190             
191             <varlistentry>
192                 
193                 <term>[R,diagevals] =spec(A)</term>
194                 
195                 <listitem>
196                     
197                     <para>
198                         
199                         対角行列r <literal>evals</literal> に固有値,
200                         
201                         <literal>R</literal>に固有ベクトルを返します.
202                         
203                     </para>
204                     
205                 </listitem>
206                 
207             </varlistentry>
208             
209             <varlistentry>
210                 
211                 <term>evals=spec(A,B)</term>
212                 
213                 <listitem>
214                     
215                     <para>行列ペンシル A - s B のスペクトル,すなわち,
216                         
217                         多項式行列 s B - Aの根,を返します.
218                         
219                     </para>
220                     
221                 </listitem>
222                 
223             </varlistentry>
224             
225             <varlistentry>
226                 
227                 <term>[alpha,beta] = spec(A,B)</term>
228                 
229                 <listitem>
230                     
231                     <para>
232                         
233                         行列ペンシル<literal>A- s B</literal>のスペクトル,
234                         
235                         すなわち,多項式行列 <literal>A - s B</literal>の根を返します.
236                         
237                         一般化固有値 alpha と beta は行列 
238                         
239                         <literal>A - alpha./beta B</literal> が特異行列となる値です.
240                         
241                         固有値は <literal>al./be</literal> により指定され,
242                         
243                         <literal>beta(i) = 0</literal>の場合,i番目の固有値は無限大となります.
244                         
245                         (<literal>B = eye(A)</literal>の場合, <literal>alpha./beta</literal>は
246                         
247                         <literal>spec(A)</literal>となります).
248                         
249                         通常,beta=0や両方がゼロの場合に関して都合が良い解釈が存在するため,
250                         
251                         (alpha,beta)の組み合わせで表されます.
252                         
253                     </para>
254                     
255                 </listitem>
256                 
257             </varlistentry>
258             
259             <varlistentry>
260                 
261                 <term>[alpha,beta,R] = spec(A,B)</term>
262                 
263                 <listitem>
264                     
265                     <para>上記に加えてペンシルの一般化右固有ベクトルとなる
266                         
267                         行列 <literal>R</literal>を返します.
268                         
269                     </para>
270                     
271                 </listitem>
272                 
273             </varlistentry>
274             
275             <varlistentry>
276                 
277                 <term>[al,be,L,R] = spec(A,B)</term>
278                 
279                 <listitem>
280                     
281                     <para>
282                         
283                         上記に加えてペンシルの一般化右および左固有ベクトルである行列
284                         
285                         <literal>L</literal> および<literal>R</literal>を返します.
286                         
287                     </para>
288                     
289                 </listitem>
290                 
291             </varlistentry>
292             
293             <varlistentry>
294                 
295                 <term>[al,be,Z] = spec(A,E)</term>
296                 
297                 <listitem>
298                     
299                     <para>
300                         
301                         一般化右固有ベクトルである行列 <literal>Z</literal> を返します.
302                         
303                     </para>
304                     
305                 </listitem>
306                 
307             </varlistentry>
308             
309             <varlistentry>
310                 
311                 <term>[al,be,Q,Z] = spec(A,E)</term>
312                 
313                 <listitem>
314                     
315                     <para>
316                         
317                         一般化右および左固有ベクトルである行列 <literal>Q</literal>
318                         
319                         および <literal>Z</literal>を返します.
320                         
321                     </para>
322                     
323                 </listitem>
324                 
325             </varlistentry>
326             
327         </variablelist>
328         
329         <para>大きな完全 / 疎行列の場合, Arnoldi モジュールを使用することができます.</para>
330         
331     </refsection>
332     
333     <refsection role="see also">
334         
335         <title>参照</title>
336         
337         <para>行列の固有値計算は Lapack ルーチンに基づいています</para>
338         
339         <itemizedlist>
340             
341             <listitem>
342                 
343                 <para>行列が対称でない場合, DGEEV および ZGEEV.</para>
344                 
345             </listitem>
346             
347             <listitem>
348                 
349                 <para>行列が対称の場合, DSYEV および ZHEEV.</para>
350                 
351             </listitem>
352             
353         </itemizedlist>
354         
355         <para>複素対象行列は複素共役の非対角項と実数の対角項を有します.</para>
356         
357         <para>ペンシル固有値計算は Lapack ルーチン
358             
359             DGGEV および ZGGEVに基づいています.
360             
361         </para>
362         
363     </refsection>
364     
365     <refsection>
366         
367         <title>実数および複素行列</title>
368         
369         <para>
370             
371             例えば evals や R のような出力変数の型は入力行列 A および B の型と
372             
373             同じである必要はないことに注意してください.
374             
375             以下のパラグラフでは、行列 A の固有値および固有ベクトルを
376             
377             計算する際の出力変数の型を解析します.
378             
379         </para>
380         
381         <itemizedlist>
382             
383             <listitem>
384                 
385                 <para>実数 A 行列</para>
386                 
387                 <itemizedlist>
388                     
389                     <listitem>
390                         
391                         <para>対称</para>
392                         
393                         <para>固有値と固有ベクトルは実数.</para>
394                         
395                     </listitem>
396                     
397                     <listitem>
398                         
399                         <para>非対称</para>
400                         
401                         <para>固有値と固有ベクトルは複素数.</para>
402                         
403                     </listitem>
404                     
405                 </itemizedlist>
406                 
407             </listitem>
408             
409             <listitem>
410                 
411                 <para>複素 A 行列</para>
412                 
413                 <itemizedlist>
414                     
415                     <listitem>
416                         
417                         <para>対称</para>
418                         
419                         <para>固有値は実数だが固有ベクトルは複素数.</para>
420                         
421                     </listitem>
422                     
423                     <listitem>
424                         
425                         <para>非対称</para>
426                         
427                         <para>固有値,固有ベクトルは複素数.</para>
428                         
429                     </listitem>
430                     
431                 </itemizedlist>
432                 
433             </listitem>
434             
435         </itemizedlist>
436         
437     </refsection>
438     
439     <refsection>
440         
441         <title>例</title>
442         
443         <programlisting role="example"><![CDATA[ 
444 // MATRIX EIGENVALUES
445 A=diag([1,2,3]);
446 X=rand(3,3);
447 A=inv(X)*A*X;
448 spec(A)
449
450 x=poly(0,'x');
451 pol=det(x*eye(3,3)-A)
452 roots(pol)
453
454 [S,X]=bdiag(A);
455 clean(inv(X)*A*X)
456
457 // PENCIL EIGENVALUES
458 A=rand(3,3);
459 [al,be,R] = spec(A,eye(A));
460 al./be
461 clean(inv(R)*A*R)  //displaying the eigenvalues (generic matrix)
462 A=A+%i*rand(A);
463 E=rand(A);
464 roots(det(A-%s*E))   //complex case
465  ]]></programlisting>
466         
467     </refsection>
468     
469     <refsection role="see also">
470         
471         <title>参照</title>
472         
473         <simplelist type="inline">
474             
475             <member>
476                 
477                 <link linkend="poly">poly</link>
478                 
479             </member>
480             
481             <member>
482                 
483                 <link linkend="det">det</link>
484                 
485             </member>
486             
487             <member>
488                 
489                 <link linkend="schur">schur</link>
490                 
491             </member>
492             
493             <member>
494                 
495                 <link linkend="bdiag">bdiag</link>
496                 
497             </member>
498             
499             <member>
500                 
501                 <link linkend="colcomp">colcomp</link>
502                 
503             </member>
504             
505             <member>
506                 
507                 <link linkend="dsaupd">dsaupd</link>
508                 
509             </member>
510             
511             <member>
512                 
513                 <link linkend="dnaupd">dnaupd</link>
514                 
515             </member>
516             
517         </simplelist>
518         
519     </refsection>
520     
521 </refentry>
522