scilab/modules/elementary_functions/help/pt_BR/elementarymatrices/diag.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  16 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
  17           xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml"
  18           xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
  19           xmlns:scilab="http://www.scilab.org" xml:id="diag" xml:lang="pt">
  20     <refnamediv>
  21         <refname>diag</refname>
  22         <refpurpose>inclusão ou extração diagonal</refpurpose>
  23     </refnamediv>
  24     <refsynopsisdiv>
  25         <title>Seqüência de Chamamento</title>
  26         <synopsis>
  27            y = diag(vm)
  28            y = diag(vm, k)
  29         </synopsis>
  30     </refsynopsisdiv>
  31     <refsection>
  32         <title>Parâmetros</title>
  33         <variablelist>
  34             <varlistentry>
  35                 <term>vm</term>
  36                 <listitem>
  37                     <para>vetor ou matriz (armazenamento cheio ou esparso)</para>
  38                 </listitem>
  39             </varlistentry>
  40             <varlistentry>
  41                 <term>k</term>
  42                 <listitem>
  43                     <para>inteiro (o valor padrão é 0)</para>
  44                 </listitem>
  45             </varlistentry>
  46             <varlistentry>
  47                 <term>y</term>
  48                 <listitem>
  49                     <para>vetor ou matriz</para>
  50                 </listitem>
  51             </varlistentry>
  52         </variablelist>
  53     </refsection>
  54     <refsection>
  55         <title>Descrição</title>
  56         <para>
  57             Para um n-vetor (linha ou coluna) <literal>vm</literal> ,
  58             <literal>diag(vm)</literal> retorna uma matriz diagonal com entradas de
  59             <literal>vm</literal> ao longo da diagonal principal.
  60         </para>
  61         <para>
  62             <literal>diag(vm,k)</literal> é uma matriz
  63             <literal>(n+abs(k))x(n+abs(k))</literal> com entradas de
  64             <literal>vm</literal> ao longo da k-ésima diagonal. <literal>k=0</literal>
  65             é a diagonal principal, <literal>k&gt;0</literal> são as diagonais
  66             superiores e <literal>k&lt;0</literal> são as diagonais inferiores.
  67         </para>
  68         <para>
  69             Para uma matriz <literal>vm</literal>, <literal>diag(vm,k)</literal>
  70             é o vetor coluna feito das entradas da k-ésima diagonal de
  71             <literal>vm</literal>. <literal>diag(vm)</literal> é a diagonal principal
  72             de <literal>vm</literal>. <literal>diag(diag(x))</literal> é a matriz
  73             diagonal.
  74         </para>
  75         <para>
  76             Se <literal>vm</literal> é uma matriz esparsa,
  77             <literal>diag(vm,k)</literal> retorna uma matriz esparsa.
  78         </para>
  79         <para>Para construir um sistema linear diagonal, use
  80             <literal>sysdiag</literal>.
  81         </para>
  82         <para>
  83             Perceba que <literal>eye(A).*A</literal> retorna uma matriz diagonal
  84             feita das entradas diagonais de <literal>A</literal>. Isto é válido para
  85             qualquer matriz (constante, de polinômios, de razões de polinômios,
  86             sistema linear em espaço de estados,...).
  87         </para>
  88     </refsection>
  89     <refsection>
  90         <title>Exemplos</title>
  91         <programlisting role="example"><![CDATA[
  92 diag([1,2])
  93
  94 A=[1,2;3,4];
  95 diag(A)  // diagonal principal
  96 diag(A,1)
  97
  98 diag(sparse(1:10))  // matriz diagonal esparsa
  99
 100 // forma de uma matriz triadiagonal de tamanho 2*m+1
 101 m=5;diag(-m:m) +  diag(ones(2*m,1),1) +diag(ones(2*m,1),-1)
 102  ]]></programlisting>
 103     </refsection>
 104     <refsection role="see also">
 105         <title>Ver Também</title>
 106         <simplelist type="inline">
 107             <member>
 108                 <link linkend="toeplitz">toeplitz</link>
 109             </member>
 110             <member>
 111                 <link linkend="eye">eye</link>
 112             </member>
 113             <member>
 114                 <link linkend="sysdiag">sysdiag</link>
 115             </member>
 116             <member>
 117                 <link linkend="spec">spec</link>
 118             </member>
 119             <member>
 120                 <link linkend="bdiag">bdiag</link>
 121             </member>
 122         </simplelist>
 123     </refsection>
 124 </refentry>