<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?> 
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>fr</LANGUAGE>
  <TITLE>pbig  </TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>April 1993  </DATE>
  <SHORT_DESCRIPTION name="pbig"> projection sur des sous-espaces propres   </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[Q,M]=pbig(A,thres,flag)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
	<PARAM_NAME>A  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : matrice réelle carrée
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
      <PARAM_ITEM>
	<PARAM_NAME>thres  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : nombre réel
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
      <PARAM_ITEM>
	<PARAM_NAME>flag  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : chaîne de caractères (<VERB>&apos;c&apos;</VERB> ou <VERB>&apos;d&apos;</VERB>)
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
      <PARAM_ITEM>
	<PARAM_NAME>Q,M  </PARAM_NAME>
	<PARAM_DESCRIPTION>
	  <SP>
	    : matrices réelles
	  </SP>
	</PARAM_DESCRIPTION> 
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
      Projection sur des sous-espaces propres de A associés aux valeurs
      propres avec partie réelle &gt;= <VERB>thres</VERB>
      (<VERB>flag=&apos;c&apos;</VERB>) ou avec module &gt;=
      <VERB>thres</VERB> (<VERB>flag=&apos;d&apos;</VERB>).
    </P>
    <P>
      La projection est définie par <VERB>Q*M</VERB>, où <VERB>Q</VERB>
      est de rang maximal, les lignes de <VERB>M</VERB> sont
      linéairement indépendantes et <VERB>M*Q=eye</VERB>.
    </P>
    <P>
      Si <VERB>flag=&apos;c&apos;</VERB>, les valeurs propres de
      <VERB>M*A*Q</VERB> = valeurs propres de <VERB>A</VERB> avec partie
      réelle &gt;= <VERB>thres</VERB>.
    </P>
    <P>
      Si <VERB>flag=&apos;d&apos;</VERB>, les valeurs propres de
      <VERB>M*A*Q</VERB> = valeurs propres de <VERB>A</VERB> avec module
      &gt;= <VERB>thres</VERB>.
    </P>
    <P>
      Si <VERB>flag=&apos;c&apos;</VERB> et si <VERB>[Q1,M1]</VERB> =
      factorisation de rang maximal (<VERB>fullrf</VERB>) de
      <VERB>eye()-Q*M</VERB> alors les valeurs propres de
      <VERB>M1*A*Q1</VERB> = valeurs propres de <VERB>A</VERB> avec
      partie réelle &lt; <VERB>thres</VERB>.
    </P>
    <P>
      Si <VERB>flag=&apos;d&apos;</VERB> et si <VERB>[Q1,M1]</VERB> =
      factorisation de rang maximal (<VERB>fullrf</VERB>) de
      <VERB>eye()-Q*M</VERB> alors les valeurs propres de
      <VERB>M1*A*Q1</VERB> = valeurs propres de <VERB>A</VERB> avec
      module &lt; <VERB>thres</VERB>.
    </P>
  </DESCRIPTION>


  <EXAMPLE><![CDATA[
    A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
    [Q,M]=pbig(A,1.5,'d');
    spec(M*A*Q)
    [Q1,M1]=fullrf(eye()-Q*M);
    spec(M1*A*Q1)
    ]]></EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>psmall</LINK> </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM> <LINK>projspec</LINK> </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM> <LINK>fullrf</LINK> </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM> <LINK>schur</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>F. Delebecque, INRIA (1988); ;   </AUTHOR>
  <USED_FUNCTIONS>
    <SP><VERB>pbig</VERB> est basée sur la forme de Schur ordonnée
    (fonction Scilab <VERB>schur</VERB>).</SP>
  </USED_FUNCTIONS>
</MAN>
