regiondiffXU

REGIONDIFFXU Computes region difference in lifted XU space

 R=regiondiffXU(Pbnd,Pn,G,W,E,Options)

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 DESCRIPTION
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 Function computes the difference between polytope Pbnd
 and union of polytopes Pn:  res=Pbnd\(U Pn) in the lifted XU space.
 In general output "res" is a polytope array containing
 non-overlapping polytopes whose union is equal to
 the difference Pbnd\(U Pn).

 Note:
 Algorithm works even for a non-minimal representation of Pn,
 However, if Pn are minimal, then code runs faster...

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 INPUT
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 Pbnd                  - polytope
 Pn                    - array of polytopes
 G,W,E                 - Matrices of the mpQP optimization problem
 Options.lpsolver      - Solver for LPs (see help mpt_solveLP)
 Options.verbose       - level of verbosity (see help mpt_init)
 Options.intersect_tol - tolerance to detect intersection
 Options.abs_tol       - absolute tolerance
 Options.tolerance     - nonegative tolerance to decide if constraint is redundant
 Options.reduce        - if region R is not given in minimal representation
                         this Option should be set to 1, default=1 (yes)
 Options.reduce_output - should the description of regions Pj={x | P.Hn{j} x <= P.Kn{j}}
                         j=1,...,P.nR, be reduced; default=1 (yes)
 Options.constructset  - if difference is not convex, should set P be
                           constructed; default=1 (yes)


 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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 res   - polytope array containing the region difference Pbnd\(U Pn)
         if the difference is empty (i.e. Pbnd is fully covered by (U Pn))
         returns an empty polytope

 see also REGIONDIFF