Home > mpt > @polytope > normalize.m

# normalize

## PURPOSE

NORMALIZE Normalizes a given polytope

## SYNOPSIS

function [P] = normalize(P,Options)

## DESCRIPTION

```NORMALIZE Normalizes a given polytope

P = normalize(P,Options)

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DESCRIPTION
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PN = NORMALIZE(P) returns normalized representation PN of a
polytope P. Polytope PN={x | H_ix <= K_i, i=1,...,nc} has the
following property: H_i' * H_i=1, for all i.

USAGE:
P=normalize(P)
P=normalize(P,Options)

NOTE:
By default, the POLYTOPE constructor performs the normalization automatically,
so there no need to use this function unless you switch the normalization
off while creating the polytope object.

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INPUT
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P                - Polytope
Options.rel_tol  - relative tolerance
Options.abs_tol  - absolute tolerance

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 normalized description

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• 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
• size SIZE Returns size of the given polytope object
This function is called by:
• analyticCenter ANALYTICCENTER Computes an analytic center of a polytope
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
• isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
• mtimes MTIMES Polytope multiplication
• normalize NORMALIZE Normalizes a given polytope
• polytope POLYTOPE Default constructor for the POLYTOPE object
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• mpt_getReachSubset MPT_GETREACHSUBSET Computes a subset of P which enters Pfin

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