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Implementation of “Parma Polyhedron Library”-functions in MATLAB
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Leo Asselborn
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Implementation of “Parma Polyhedron Library”-functions in MATLAB
1.
2.
3.
Parma Polyhedron Library
4.
Challenges in detail
5.
Benchmarking results
6.
7.
8.
n-dimensions
9.
2- polytope: polygon
10.
11.
Convex polytopes
12.
Star polytopes
13.
Abstract polytopes
14.
Self-dual polytopes
15.
16.
(V-representation)
17.
Half space representation
18.
19.
20.
Fast numerical algorithms
21.
Easy building of
prototypes
22.
23.
Used to create
convex polytopes
24.
Very user friendly
(you write x + 2*y + 5*z <= 7 when you mean it)
25.
Efficient
26.
Very precise by
using GMP data types (precision is limited by the available memory)
27.
28.
External interface function
which allow to interface with C/C++ or Fortran subroutines.
29.
30.
Speed
31.
32.
void mexFunction( int
nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]){ if ((nrhs == 2)&&(nlhs == 1)){ double *Input0 = mxGetPr(prhs[1]); double *Input1 = mxGetPr(prhs[2]); double *Return_arg = mxGetPr(plhs[0]); Return_arg[0] = Input0[0] + Input1[0]; } }
33.
34.
35.
36.
Compile to .mexglx
files with Eclipse
37.
Find a structure
to be easily maintained Double mpz_class Linear expression inequations Constraint System Polytope Double mpz_class Linear expression inequations Constraint System mxArray mxArray Polytope computation
38.
39.
40.
http://en.wikipedia.org/wiki/File:3dpoly.svg
41.
http://t1.gstatic.com/images?q=tbn:luK1qGow7LqkwM:http://megashareslink.com/wp-content/uploads/2009/04/matlab_logo.gif&t=1
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