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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/svd.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>svd</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="svd">  singular value decomposition</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>s=svd(X)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[U,S,V]=svd(X)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[U,S,V]=svd(X,0) (obsolete)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[U,S,V]=svd(X,&quot;e&quot;)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[U,S,V,rk]=svd(X [,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>X</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: a 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>s</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real vector (singular values)</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>S</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real diagonal matrix (singular values)</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>U,V</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: orthogonal or unitary square matrices (singular vectors).</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</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><VERB>[U,S,V] = svd(X)</VERB> produces a diagonal matrix
 
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    <VERB>S</VERB> , of the same dimension as <VERB>X</VERB> and with
 
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    nonnegative diagonal elements in decreasing order, and unitary
 
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    matrices <VERB>U</VERB> and <VERB>V</VERB> so that <VERB>X =
 
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    U*S*V'</VERB>.</P>
 
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    <P><VERB>[U,S,V] = svd(X,0)</VERB> produces the &quot;economy
 
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    size&quot; decomposition. If <VERB>X</VERB> is m-by-n with m &gt;
 
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    n, then only the first n columns of <VERB>U</VERB> are computed
 
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    and <VERB>S</VERB> is n-by-n.</P>
 
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    <P><VERB>s = svd(X)</VERB> by itself, returns a vector <VERB>s</VERB>
 
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    containing the singular values.</P>
 
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    <P><VERB>[U,S,V,rk]=svd(X,tol)</VERB> gives in addition <VERB>rk</VERB>, the numerical rank of <VERB>X</VERB> i.e. the number of 
 
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    singular values larger than <VERB>tol</VERB>.</P>
 
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    <P>
 
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    The default value of <VERB>tol</VERB> is the same as in <VERB>rank</VERB>.</P>
 
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  </DESCRIPTION>
 
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  <EXAMPLE>
 
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<![CDATA[
 
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X=rand(4,2)*rand(2,4)
 
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svd(X)
 
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sqrt(spec(X*X'))
 
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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>rank</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>colcomp</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>sva</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>spec</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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  <USED_FUNCTIONS>
 
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    <P>
 
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   svd decompositions are based on  the Lapack routines DGESVD for
 
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   real matrices and  ZGESVD for the complex case.</P>
 
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  </USED_FUNCTIONS>
 
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</MAN>