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# reduce

## PURPOSE

REDUCE Reduces the polytope by removing redundant inequalities

## SYNOPSIS

function [P,keptrows]=reduce(P,Options,lambda)

## DESCRIPTION

```REDUCE Reduces the polytope by removing redundant inequalities

[P,keptrows] = reduce(P,Options,lambda)

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DESCRIPTION
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[P,keptrows]=REDUCE(P,OPTIONS) computes the minimal representation of the
polytope P by eliminating all redundant constraints. The reduction of P is
implemented by solving one LP for each facet.

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INPUT
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P                     - Polytope
Options.lpsolver      - LP solver to be used (see help mpt_solveLP)
Options.abs_tol       - absolute tolerance
Options.calculatebox  - Use a bounding box to discard certain hyperplanes a
priori (1: use BoundingBox)
lambda                - Optional: Set of lagrange multipliers from chebyball;
If available, this speeds up the reduction procedure.

Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used

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OUTPUT
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P         - polytope in reduced description
keptrows  - indices of hyperplanes which are non-redundand

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
• normalize NORMALIZE Normalizes a given polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• size SIZE Returns size of the given polytope object
• unique UNIQUE Removes redundant entries from a polytope array
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_solveLPs MPT_SOLVELPS Interface to various LP solvers ("safe" version)
This function is called by:
• analyticCenter ANALYTICCENTER Computes an analytic center of a polytope
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• domain DOMAIN Computes polytope that is mapped to an another polytope using affine map
• envelope ENVELOPE Computes envelope of n polytopes
• eq EQ Checks if two polytopes are equal
• extreme EXTREME Calculates extreme points of a given polytope
• facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
• isbounded ISBOUNDED Checks if a polytope is bounded
• lt LT Checks if polytope P is a strict subset of polytope Q
• minus MINUS Pontryagin difference
• mtimes MTIMES Polytope multiplication
• plot PLOT Plots polytopes in 2D or 3D
• plus PLUS Minkowski sum of two polytopes
• polytope POLYTOPE Default constructor for the POLYTOPE object
• projection PROJECTION Projection of a polytope or a polytope array
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• regiondiff REGIONDIFF Region difference
• uminus UMINUS Unary minus for a polytope
• union UNION convex union computation
• uplus UPLUS Unary plus for a polytope
• mpt_getReachSubset MPT_GETREACHSUBSET Computes a subset of P which enters Pfin
• mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf
• mpt_mplp_ver3 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver6 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_boolMinTime MPT_BOOLMINTIME Computes minimum time controller for systems with discrete inputs
• mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
• mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs
• mpt_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
• tg_polyreduce
• hull HULL Converts vertices/polytope array into an H-representation polytope
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

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