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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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man/fr/linear/randpencil.xml
 
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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
 
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
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<MAN>
 
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  <LANGUAGE>eng</LANGUAGE>
 
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  <TITLE>quaskro</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="randpencil"> random pencil</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>F=randpencil(eps,infi,fin,eta)  </CALLING_SEQUENCE_ITEM>
 
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  </CALLING_SEQUENCE>
 
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  <PARAM>
 
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    <PARAM_INDENT>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>eps</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: vector of integers</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>infi</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: vector of integers</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>fin</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real vector, or monic polynomial, or vector of monic polynomial</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>eta</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: vector of integers</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>F</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real matrix pencil <VERB>F=s*E-A</VERB>  (<VERB>s=poly(0,'s')</VERB>)</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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    </PARAM_INDENT>
 
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  </PARAM>
 
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  <DESCRIPTION>
 
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    <P>
 
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    Utility function.
 
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    <VERB>F=randpencil(eps,infi,fin,eta)</VERB> returns a random pencil <VERB>F</VERB>
 
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    with given Kronecker structure. The structure is given by:
 
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    <VERB>eps=[eps1,...,epsk]</VERB>: structure of epsilon blocks (size eps1x(eps1+1),....)
 
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    <VERB>fin=[l1,...,ln]</VERB>  set of finite eigenvalues (assumed real)  (possibly [])
 
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    <VERB>infi=[k1,...,kp]</VERB> size of J-blocks at infinity
 
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    <VERB>ki&gt;=1</VERB>  (infi=[] if no J blocks).
 
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    <VERB>eta=[eta1,...,etap]</VERB>: structure ofeta blocks (size eta1+1)xeta1,...)</P>
 
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    <P><VERB>epsi</VERB>'s should be &gt;=0, <VERB>etai</VERB>'s should be &gt;=0, <VERB>infi</VERB>'s should 
 
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    be &gt;=1.</P>
 
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    <P>
 
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    If <VERB>fin</VERB> is a (monic) polynomial, the finite block admits the roots of 
 
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    <VERB>fin</VERB> as eigenvalues.</P>
 
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    <P>
 
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    If <VERB>fin</VERB> is a vector of polynomial, they are the finite elementary
 
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    divisors of <VERB>F</VERB> i.e. the roots of <VERB>p(i)</VERB> are finite
 
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    eigenvalues of <VERB>F</VERB>.</P>
 
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  </DESCRIPTION>
 
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  <EXAMPLE>
 
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<![CDATA[
 
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F=randpencil([0,1],[2],[-1,0,1],[3]);
 
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[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F);
 
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Qd, Zd
 
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s=poly(0,'s');
 
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F=randpencil([],[1,2],s^3-2,[]); //regular pencil
 
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det(F)
 
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 ]]>
 
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  </EXAMPLE>
 
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  <SEE_ALSO>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>kroneck</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>pencan</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>penlaur</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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</MAN>