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