scilab/modules/linear_algebra/help/pt_BR/linear/linsolve.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:ns4="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="linsolve" xml:lang="pt">
  17     <refnamediv>
  18         <refname>linsolve</refname>
  19         <refpurpose>solucionador de equações lineares</refpurpose>
  20     </refnamediv>
  21     <refsynopsisdiv>
  22         <title>Seqüência de Chamamento</title>
  23         <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
  24     </refsynopsisdiv>
  25     <refsection>
  26         <title>Parâmetros</title>
  27         <variablelist>
  28             <varlistentry>
  29                 <term>A</term>
  30                 <listitem>
  31                     <para>
  32                         uma matriz <literal>na x ma</literal> de reais (possivelmente
  33                         esparsa)
  34                     </para>
  35                 </listitem>
  36             </varlistentry>
  37             <varlistentry>
  38                 <term>b</term>
  39                 <listitem>
  40                     <para>
  41                         um vetor <literal>na x 1</literal> (mesma dimensão de linha de
  42                         <literal>A</literal>)
  43                     </para>
  44                 </listitem>
  45             </varlistentry>
  46             <varlistentry>
  47                 <term>x0</term>
  48                 <listitem>
  49                     <para>um vetor de reais </para>
  50                 </listitem>
  51             </varlistentry>
  52             <varlistentry>
  53                 <term>kerA</term>
  54                 <listitem>
  55                     <para>
  56                         uma matriz <literal>ma x k</literal> de reais
  57                     </para>
  58                 </listitem>
  59             </varlistentry>
  60         </variablelist>
  61     </refsection>
  62     <refsection>
  63         <title>Descrição</title>
  64         <para>
  65             <literal>linsolve</literal> computa todas as soluções para <literal>
  66                 A*x+b=0
  67             </literal>
  68             .
  69         </para>
  70         <para>
  71             <literal>x0</literal> é uma solução particular (se houver) e
  72             <literal> kerA= </literal>núcleo de <literal>A</literal>. Qualquer
  73             <literal>x=x0+kerA*w</literal> com <literal>w</literal> arbitrário
  74             satisfaz <literal> A*x+b=0</literal>.
  75         </para>
  76         <para>
  77             Se um compatible <literal>x0</literal> compatível é dado na entrada,
  78             <literal>x0</literal> é retornado. Senão, um <literal>x0</literal>,
  79             compatível é retornado, se houver.
  80         </para>
  81     </refsection>
  82     <refsection>
  83         <title>Exemplos</title>
  84         <programlisting role="example"><![CDATA[
  85 A=rand(5,3)*rand(3,8);
  86 b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //b comatível
  87 b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //b incompatível
  88 A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x é único
  89
  90 // A benchmark of sparse linear solver
  91
  92 [A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/demos/bcsstk24.rsa");
  93
  94 b = zeros(size(A,1),1);
  95
  96 tic();
  97 res = umfpack(A,'\',b);
  98 mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
  99
 100 tic();
 101 res = linsolve(A,b);
 102 mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
 103
 104 tic();
 105 res = A\b;
 106 mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
 107  ]]></programlisting>
 108     </refsection>
 109     <refsection>
 110         <title> Ver Também</title>
 111         <simplelist type="inline">
 112             <member>
 113                 <link linkend="inv">inv</link>
 114             </member>
 115             <member>
 116                 <link linkend="pinv">pinv</link>
 117             </member>
 118             <member>
 119                 <link linkend="colcomp">colcomp</link>
 120             </member>
 121             <member>
 122                 <link linkend="im_inv">im_inv</link>
 123             </member>
 124             <member>
 125                 <link linkend="backslash">backslash</link>
 126             </member>
 127             <member>
 128                 <link linkend="umfpack">umfpack</link>
 129             </member>
 130         </simplelist>
 131     </refsection>
 132 </refentry>