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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/eng/linear/fullrf.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>fullrf</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="fullrf"> full rank factorization</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>[Q,M,rk]=fullrf(A,[tol])  </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>A</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real or complex matrix</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>tol</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real number (threshold for rank determination)</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>Q,M</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real or complex matrix</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>rk</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: integer (rank of <VERB>A</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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    Full rank factorization : <VERB>fullrf</VERB> returns <VERB>Q</VERB> and <VERB>M</VERB> such
 
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    that <VERB>A = Q*M</VERB>
 
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    with range(<VERB>Q</VERB>)=range(<VERB>A</VERB>) and ker(<VERB>M</VERB>)=ker(<VERB>A</VERB>),
 
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    <VERB>Q</VERB> full column rank , <VERB>M</VERB> full row rank,
 
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    <VERB>rk</VERB> = rank(<VERB>A</VERB>) = #columns(<VERB>Q</VERB>) = #rows(<VERB>M</VERB>).</P>
 
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    <P><VERB>tol</VERB> is an optional real parameter (default value is <VERB>sqrt(%eps)</VERB>).
 
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    The rank <VERB>rk</VERB> of <VERB>A</VERB> is defined as the number of singular values
 
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    larger than <VERB>norm(A)*tol</VERB>.</P>
 
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    <P>
 
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    If A is symmetric, <VERB>fullrf</VERB> returns <VERB>M=Q'</VERB>.</P>
 
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  </DESCRIPTION>
 
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  <EXAMPLE>
 
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<![CDATA[
 
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A=rand(5,2)*rand(2,5);
 
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[Q,M]=fullrf(A);
 
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norm(Q*M-A,1)
 
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[X,d]=rowcomp(A);Y=X';
 
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svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
 
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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>svd</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>qr</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>fullrfk</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>rowcomp</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>colcomp</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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  <AUTHOR>F.D.;   </AUTHOR>
 
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</MAN>