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<?xml version="1.0" encoding="UTF-8"?>
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* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
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* Copyright (C) 2008 - INRIA
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* This file must be used under the terms of the CeCILL.
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* This source file is licensed as described in the file COPYING, which
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* you should have received as part of this distribution. The terms
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* are also available at
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* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="ereduc">
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<refname>ereduc</refname>
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<refpurpose> computes matrix column echelon form by qz transformations</refpurpose>
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<title>Calling Sequence</title>
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<synopsis>[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)</synopsis>
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<title>Arguments</title>
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<para>m x n matrix with real entries.</para>
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<para>real positive scalar.</para>
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<para>column echelon form matrix</para>
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<para>m x m unitary matrix</para>
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<para>n x n unitary matrix</para>
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<para>vector of indexes,</para>
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<literal>ISTAIR(i) = + j</literal> if the boundary element <literal>E(i,j)</literal> is a corner point.
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<literal>ISTAIR(i) = - j</literal> if the boundary element <literal>E(i,j)</literal> is not a corner point.
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<literal>(i=1,...,M)</literal>
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<para>integer, estimated rank of the matrix</para>
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<title>Description</title>
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Given an <literal>m x n</literal> matrix <literal>X</literal> (not necessarily regular) the function
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ereduc computes a unitary transformed matrix <literal>E=Q*X*Z</literal> which is in
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column echelon form (trapezoidal form). Furthermore the rank of
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matrix <literal>X</literal> is determined.
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<title>Examples</title>
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<programlisting role="example"><![CDATA[
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[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)
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<refsection role="see also">
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<title>See Also</title>
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<simplelist type="inline">
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<link linkend="fstair">fstair</link>