25c72b86a09c2faf098a29856152b112642a3add
[scilab.git] / scilab / modules / linear_algebra / help / pt_BR / pencil / kroneck.xml
1 <?xml version="1.0" encoding="ISO-8859-1"?>
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16 <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="kroneck" xml:lang="en">
17     <refnamediv>
18         <refname>kroneck</refname>
19         <refpurpose>forma de Kronecker de feixe de matrizes</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title> Seqüência de Chamamento </title>
23         <synopsis>[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F)
24             [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(E,A)
25         </synopsis>
26     </refsynopsisdiv>
27     <refsection>
28         <title>Parâmetros</title>
29         <variablelist>
30             <varlistentry>
31                 <term>F</term>
32                 <listitem>
33                     <para>
34                         feixe de matrizes de reais <literal>F=s*E-A</literal>
35                     </para>
36                 </listitem>
37             </varlistentry>
38             <varlistentry>
39                 <term>E,A</term>
40                 <listitem>
41                     <para>duas matrizes de reais de mesma dimensão</para>
42                 </listitem>
43             </varlistentry>
44             <varlistentry>
45                 <term>Q,Z</term>
46                 <listitem>
47                     <para>duas matrizes quadradas ortogonais </para>
48                 </listitem>
49             </varlistentry>
50             <varlistentry>
51                 <term>Qd,Zd</term>
52                 <listitem>
53                     <para>dois vetores de inteiros </para>
54                 </listitem>
55             </varlistentry>
56             <varlistentry>
57                 <term>numbeps,numeta</term>
58                 <listitem>
59                     <para>dois vetores de inteiros</para>
60                 </listitem>
61             </varlistentry>
62         </variablelist>
63     </refsection>
64     <refsection>
65         <title>Descrição</title>
66         <para>
67             Forma de Kronecker de feixe de matrizes: <literal>kroneck</literal>
68             computa duas matrizes ortogonais <literal>Q, Z</literal> que põem o feixe
69             <literal>F=s*E -A</literal> na forma triangular superior:
70         </para>
71         <programlisting role=""><![CDATA[ 
72            | sE(eps)-A(eps) |        X       |      X     |      X        |
73            |----------------|----------------|------------|---------------|
74            |        O       | sE(inf)-A(inf) |      X     |      X        |
75 Q(sE-A)Z = |---------------------------------|----------------------------|
76            |                |                |            |               |
77            |        0       |       0        | sE(f)-A(f) |      X        |
78            |--------------------------------------------------------------|
79            |                |                |            |               |
80            |        0       |       0        |      0     | sE(eta)-A(eta)|
81  ]]></programlisting>
82         <para>As dimensões dos quatro blocos são dadas por:</para>
83         <para>
84             <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x
85                 Zd(2)
86             </literal>
87             ,<literal>f = Qd(3) x Zd(3)</literal>,
88             <literal>eta=Qd(4)xZd(4)</literal>
89         </para>
90         <para>
91             O bloco <literal>inf</literal> contém modos infinitos de
92             feixes.
93         </para>
94         <para>
95             O bloco <literal>f</literal> contém modos finitos de feixes.
96         </para>
97         <para>A estrutura dos blocos epsilon e eta é dada por </para>
98         <para>
99             <literal>numbeps(1)</literal> = <literal>#</literal> de blocos eps
100             de tamanho 0 x 1
101         </para>
102         <para>
103             <literal>numbeps(2)</literal> = <literal>#</literal> de blocos eps
104             de tamanho 1 x 2
105         </para>
106         <para>
107             <literal>numbeps(3)</literal> = <literal>#</literal> de blocos eps
108             de tamanho 2 x 3 etc...
109         </para>
110         <para>
111             <literal>numbeta(1)</literal> = <literal>#</literal> de blocos eta
112             de tamanho 1 x 0
113         </para>
114         <para>
115             <literal>numbeta(2)</literal> = <literal>#</literal> de blocos eta
116             de tamanho 2 x 1
117         </para>
118         <para>
119             <literal>numbeta(3)</literal> = <literal>#</literal> de blocos eta
120             de tamanho 3 x 2 etc...
121         </para>
122         <para>O código foi retirado de T. Beelen (Slicot-WGS group).</para>
123     </refsection>
124     <refsection>
125         <title>Exemplos</title>
126         <programlisting role="example"><![CDATA[ 
127 F=randpencil([1,1,2],[2,3],[-1,3,1],[0,3]);
128 Q=rand(17,17);Z=rand(18,18);F=Q*F*Z;
129 //feixe aleatório com eps1=1,eps2=1,eps3=1; 2 blocos J @ infty (infinito)
130 //com dimensões 2 e 
131 //3 autovalores finitos em -1,3,1 e eta1=0,eta2=3
132 [Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F);
133 [Qd(1),Zd(1)]    //parte eps. é sum(epsi) x (sum(epsi) + número de epsi) (sum="soma")
134 [Qd(2),Zd(2)]    //parte infinita
135 [Qd(3),Zd(3)]    //parte finita
136 [Qd(4),Zd(4)]    //parte eta é (sum(etai) + number(eta1)) x sum(etai) (number=número)
137 numbeps
138 numbeta
139  ]]></programlisting>
140     </refsection>
141     <refsection>
142         <title> Ver Também</title>
143         <simplelist type="inline">
144             <member>
145                 <link linkend="gschur">gschur</link>
146             </member>
147             <member>
148                 <link linkend="gspec">gspec</link>
149             </member>
150             <member>
151                 <link linkend="systmat">systmat</link>
152             </member>
153             <member>
154                 <link linkend="pencan">pencan</link>
155             </member>
156             <member>
157                 <link linkend="randpencil">randpencil</link>
158             </member>
159             <member>
160                 <link linkend="trzeros">trzeros</link>
161             </member>
162         </simplelist>
163     </refsection>
164 </refentry>