Man page of fel

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# fel

Section: lrslib 7.3 (1)
Updated: 2024.1.10
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### Name

fel - Project an H-representation or V-representation onto a subset of columns.

### Synopsis

fel [input-file] [output-file]
mpirun -np [procs] mplrs -fel [input-file] [output-file] [option...]

### Description

fel is an alias of lrs which can also perform these functions via
  the eliminate and project options.

  H-representation.
  The input is projected onto a given set of columns using Fourier-Motzkin elimination. An H-representation is output after each iteration. mplrs -fel is a fully parallel version that performs one iteration only, see mplrs(1).
  V-representation.
  The specified columns are extracted and redundant rows are removed. The output can be can be piped directly into lrs. Not implemented in mplrs.

  ### Options

  These options are placed after the end statement.

  eliminate k i_1 i_2 ... i_k (new in v7.2)
  (H-representation) Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration.
  (V-representation) Delete the k given columns from the input matrix and remove redundancies (cf. extract where redundancies are not removed).
  Column indices are between 1 and n-1 and column zero cannot be eliminated. The output is a valid lrs input file.

  project k i_1 i_2 ... i_k (new in v7.2)
  (H-representation) Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated using a heuristic which chooses the column which minimizes the product of the number of positive and negative entries. Redundancy is removed after each iteration using linear programming.
  (V-representation) Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. extract where redundancies are not removed).
  The output as a valid lrs input file.

  See also extract in lrs(1).

  verbose

  For an H-representation give, for each iteration, statistics on how many new inequaties were created and how many of these were redundant. See Example below.

  ### Example

  (1) Project onto columns 1 and 3 in an H-representation

  % cat cube.ine
  cube.ine
  H-representation
  begin
  6 4 rational
  1 1 0 0
  1 0 1 0
  1 0 0 1
  1 -1 0 0
  1 0 0 -1
  1 0 -1 0
  end
  project 2 1 3
  verbose

  % fel cube.ine
  fel:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
  *Input taken from cube.ine
  cube
  *switching to fel mode
  *project 2 1 3
  *after removing column 2
  *checking for redundant rows only
  H-representation
  begin
  4 3 rational
  0 1 0
  1 -1 0
  1 0 -1
  -1 0 1
  end
  *number of number after number of remaining column
  *inequalties removing col redundancies rows removed
  * 7 6 2 4 2
  --------------------------------------------------------------------

  *original vars remaining: 1 3

  (2) Eliminate columns 1,2,3 from a V-representation

  % cat cp4.ext
  V-representation
  begin
  8 7 rational
  1 0 0 0 0 0 0
  1 0 1 1 1 1 0
  1 1 1 0 0 1 1
  1 1 0 0 1 1 0
  1 0 0 1 0 1 1
  1 1 1 1 0 0 0
  1 0 1 0 1 0 1
  1 1 0 1 1 0 1
  end
  eliminate 3 1 2 3
  % lrs cp4.ext
  lrs:lrslib_v.7.3_2024.1.12(64bit,lrslong.h,hybrid_arithmetic)
  *Input taken from cp4.ext
  cp4
  *switching to fel mode
  *eliminate 3 1 2 3
  *checking for redundant rows only
  V-representation
  begin
  4 4 rational
  1 1 1 0
  1 0 1 1
  1 0 0 0
  1 1 0 1
  end
  *columns retained: 0 4 5 6

  ### Notes

  1.
    FAQ page
      https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
  2.
    User's guide for lrslib
      http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html

  ### Author

  David Avis <avis at cs dot mcgill dot ca >

  ### See also

  lrs(1), mplrs(1), lrslib(5),

  ## Index

  Name
  Synopsis
  Description
  Options
  Example
  Notes
  Author
  See also

  This document was created by man2html, using the manual pages.
  Time: 07:33:14 GMT, January 31, 2024