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Content-type: text/html; charset=UTF-8
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<HTML><HEAD><TITLE>Man page of redund|minrep</TITLE>
</HEAD><BODY>
<H1>redund|minrep</H1>
Section: lrslib 7.3 (1)<BR>Updated: 2024.1.10 <BR><A HREF="#index">Index</A>
<A HREF="../index.html">Return to Main Contents</A><HR>
<A NAME="lbAB"> </A>
<H3>Name</H3>
redund|minrep - Remove redundant inequalities from an H-representation or redundant
vertices (non-extreme points) from a V-representation. <B>minrep</B> also identifies hidden
linearities.
<A NAME="lbAC"> </A>
<H3>Synopsis</H3>
<DL COMPACT>
<DT>
<B>redund</B> <I>[input-file] [output-file]</I>
<DT>
<B>minrep</B> <I>[input-file] [output-file]</I>
<DT>
<B>mpirun</B> -np [procs] <B>mplrs -minrep</B> <I>[input-file] [output-file] [option...]</I>
</DL>
<A NAME="lbAD"> </A>
<H3>Description</H3>
<P>
<B>redund</B> and <B>minrep</B> are aliases to <B>lrs</B> which is part of
<DD>the C library <B><A HREF="../man5/lrslib.5.html">lrslib</A>(5)</B>.
This functionality can also be performed by
<B>lrs</B> directly by using the options described below.
All computations are done in exact arithmetic. For input file descriptions
see <B><A HREF="../man1/lrs.1.html">lrs</A>(1)</B>.
A parallel version of <B>minrep</B>
is given by <B>mplrs -minrep</B>.
The <B>-redund</B> option performs the same function and is retained for legacy.
(see <B><A HREF="../man1/mplrs.1.html">mplrs</A>(1)</B>)
<P>
<I>redund</I>
<BR>
<I>H-representation:</I>
redundant inequalities in an input H-representation are removed and
the remaining inequalities output.
Hidden linearities
are not detected unless the <B>testlin</B> option is included,
in which case the output is a minimum representation
and the dimension is reported.
<BR>
<I>V-representation:</I>
outputs all extreme points and extreme rays, often called the
<I>convex hull</I> problem.
The <B>testlin</B> option cause linearities to be detected and explicitly
output.
<BR>
Outputs can be piped directly into <I>lrs</I>.
<I>redund</I> is a link to <I>lrs</I> which can also perform these functions via
the <B>testlin</B>, <B>redund</B> and <B>redund_list</B> options.
<B>mplrs -redund</B> always sets the <B>testlin</B> option, so always produces
minimum representations.
<P>
<I>minrep</I>
<BR>
Equivalent to <B>redund</B> with the <B>testlin</B> option.
<P>
<P>
With no options minrep|redund will process the entire input file.
<P>
<B>redund start end </B>
<BR>
Check input lines with line numbers from start to end and remove any redundant lines.
<BR>
<B>redund 0 0</B> will check all input lines.
<P>
<B>redund_list k i_1 i_2 ... i_k</B>
<BR>
Check the k input line numbers with indices i_1 i_2 ... i_k
and remove any redundant lines.
<P>
<B>testlin</B> <B>(before the begin line only)</B> (new 7.3)
<BR>
An LP test will be made for hidden linearities at the beginning of the run and is reported.
If there are no hidden linearities
one LP per constraint tests for redundancy. (<I>mplrs</I> can be run with no verification step.)
If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies.
In both cases
the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates)
and the dimension is reported.
(<I>mplrs</I> will find all linearities but some non redundant inequalities may be eliminated, so a second run is required.)
<P>
<B>verbose</B>
<BR>
As each input line is checked a message is printed telling its status
<BR>
<BR> *nr :non-redundant
<BR> *re :redundant
<BR> *sr :strongly redundant
<BR>
For an H-representation strongly redundant means the feasible
region lies in its open half-space. For a V-representation it means that the point
lies in the (relative) interior of the convex hull.
<BR>
In addition <I>minrep</I> may report
<BR> *li :linearity
<A NAME="lbAE"> </A>
<H3>Examples</H3>
<P>
(1) Remove hidden linearities and minimum representation of an H-representation.
<BR> % cat cube.ine
<BR> H-representation
<BR> begin
<BR> 7 4 rational
<BR> 0 1 0 0
<BR> 0 0 1 0
<BR> 0 0 0 1
<BR> 1 -1 0 0
<BR> 1 0 -1 0
<BR> 1 0 0 -1
<BR> -1 0 0 1
<BR> end
<BR> verbose
<BR>
<BR> % minrep cube.ine
<BR> minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
<BR> *Input taken from cube.ine
<BR> *hidden linearities exist
<BR> *finding minimum representation
<BR> *nr 0 1 0 0
<BR> *nr 0 0 1 0
<BR> *sr 0 0 0 1
<BR> *nr 1 -1 0 0
<BR> *nr 1 0 -1 0
<BR> *li 1 0 0 -1
<BR> *li-1 0 0 1
<BR> *linearity in row=6 removed or in cobasis, independent
<BR> *linearity in row=7 dependent, made redundant
<BR> H-representation
<BR> linearity 1 1
<BR> begin
<BR> 5 4 rational
<BR> 1 0 0 -1
<BR> 0 1 0 0
<BR> 0 0 1 0
<BR> 1 -1 0 0
<BR> 1 0 -1 0
<BR> end
<BR>
<BR> *input had 7 rows and 4 columns
<BR> * 2 redundant row(s) found
<BR> 3 7
<BR> * 1 hidden linearity found
<BR>
<P>
(2) Compute the extreme points of a set of 10 points in R^3
<P>
<BR> % cat c.ext
<BR> V-representation
<BR> begin
<BR> 10 4 rational
<BR> 1 1 1 1
<BR> 1 0 1 1
<BR> 1 1/2 0 1/3
<BR> 1 1 1 0
<BR> 1 0 1 0
<BR> 1 1 0 0
<BR> 1 0 0 0
<BR> 1 0 1/3 1/4
<BR> 1 1 0 1
<BR> 1 0 0 1
<BR> end
<P>
<BR> % redund c.ext
<P>
<BR> *redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic)
<BR> *Input taken from c.ext
<BR> V-representation
<BR> begin
<BR> 8 4 rational
<BR> 1 1 1 1
<BR> 1 0 1 1
<BR> 1 1 1 0
<BR> 1 0 1 0
<BR> 1 1 0 0
<BR> 1 0 0 0
<BR> 1 1 0 1
<BR> 1 0 0 1
<BR> end
<BR> *Input had 10 rows and 4 columns
<BR> * 2 redundant row(s) found:
<BR> 3 8
<P>
<A NAME="lbAF"> </A>
<H3>Notes</H3>
<DL COMPACT>
<DT> 1.<DD>
FAQ page
<DL COMPACT><DT><DD>
<A HREF="https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html">https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html</A>
</DL>
<DT>2.<DD>
redund: extreme point enumeration and eliminating redundant inequalities
<DL COMPACT><DT><DD>
<A HREF="http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund">http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund</A>
</DL>
<DT>3.<DD>
User's guide for lrslib
<DL COMPACT><DT><DD>
<A HREF="http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html">http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html</A>
</DL>
</DL>
<A NAME="lbAG"> </A>
<H3>Author</H3>
David Avis <avis at cs dot mcgill dot ca >
<A NAME="lbAH"> </A>
<H3>See also</H3>
<B><A HREF="../man1/lrs.1.html">lrs</A></B>(1),
<B><A HREF="../man1/mplrs.1.html">mplrs</A></B>(1),
<B><A HREF="../man5/lrslib.5.html">lrslib</A></B>(5),
<P>
<HR>
<A NAME="index"> </A><H2>Index</H2>
<DL>
<DL>
<DT><A HREF="#lbAB">Name</A><DD>
<DT><A HREF="#lbAC">Synopsis</A><DD>
<DT><A HREF="#lbAD">Description</A><DD>
<DT><A HREF="#lbAE">Examples</A><DD>
<DT><A HREF="#lbAF">Notes</A><DD>
<DT><A HREF="#lbAG">Author</A><DD>
<DT><A HREF="#lbAH">See also</A><DD>
</DL>
</DL>
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Time: 07:33:14 GMT, January 31, 2024
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