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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>fr</LANGUAGE>
  <TITLE>givens  </TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>April 1993  </DATE>
  <SHORT_DESCRIPTION name="givens"> Transformation de Givens  </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
  <CALLING_SEQUENCE_ITEM>U=givens(xy)  </CALLING_SEQUENCE_ITEM>
  <CALLING_SEQUENCE_ITEM>U=givens(x,y)  </CALLING_SEQUENCE_ITEM>
  <CALLING_SEQUENCE_ITEM>[U,c]=givens(xy)  </CALLING_SEQUENCE_ITEM>
  <CALLING_SEQUENCE_ITEM>[U,c]=givens(x,y)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
 <PARAM_INDENT>
  <PARAM_ITEM>
  <PARAM_NAME>x,y  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : deux nombres réels ou complexes
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>xy  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    :  vecteur colonne réel ou complexe à deux composantes
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>U  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    : matrice unitaire 2 x 2
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
  <PARAM_ITEM>
  <PARAM_NAME>c  </PARAM_NAME>
  <PARAM_DESCRIPTION>
  <SP>
    :  vecteur colonne réel ou complexe à deux composantes
</SP>
  </PARAM_DESCRIPTION> 
  </PARAM_ITEM>
 </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
  <P>
    <VERB>U = givens(x, y)</VERB> ou <VERB>U = givens(xy)</VERB> avec <VERB>xy = [x;y]</VERB>
    renvoie <VERB>U</VERB> une matrice unitaire <VERB>2</VERB>x<VERB>2</VERB> telle que :
  </P>
  <P>
    <VERB>U*xy=[r;0]=c</VERB>.
  </P>
  <P>
    Notez que <VERB>givens(x,y)</VERB> et <VERB>givens([x;y])</VERB> sont équivalents.
  </P>
  </DESCRIPTION>
  <EXAMPLE><![CDATA[
A=[3,4;5,6];
U=givens(A(:,1));
U*A
 ]]></EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>qr</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
