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MaxPlusAndPetrinet >> MaxPlusAndPetrinet > maxplusmaxalgolpoly

maxplusmaxalgolpoly

Max-plus algebra eigenvalue and eigenvector

Calling Sequence

[l,v,d] = maxplusmaxalgolpoly(A)

Parameters

A
: a input matrix polynomial have size mxnxp
l
: an eigenvalue of the matrix polynomial A.
v
: a corresponding eigenvector of the matrix polynomial A .
d

: a positve integer number that represents the period of vectors

x(q),x(q+1),⋯,x(p-1),x(p), where d = p-q and x(p) = l⊗x(q).

Description

The function valid for both an irreducible and a reducible matrix A as long as the cycle time vector of matrix A contains all elements equal to the same constant, and returns eigenvector and a unique corresponding eigenvalue of matrix A. If the condition is not satisfied the function returns error. And if numerical error this function maxplusmaxalgol still work but A⊗v≠l⊗v and the norm of A⊗v - l⊗v given by norm(A⊗x - l⊗v)≤4.019D-14 .

For details see: Subiono and J.van der Woude (2000); "Power algorithms for (max,+)- and bipartite (min,max,+)-systems"; DEDS, vol.10, pp.369-389, 2000.

If the matrix A irreducible, instead of use function maxalgol, the time computation will more faster.

Examples

A=maxpluszeros(6,6);

A(:,:,2) =[-%inf  3. -%inf -%inf 7. -%inf;
       2. -%inf 6. -%inf 7. 2.;
       -%inf 7. 8. 9. -%inf -%inf;
       -%inf -%inf -%inf 1. 2. -%inf;
       8. -%inf 7. -%inf -%inf 2.;
       0. -%inf -%inf 6. 5. -%inf];
[l,v,d] = maxplusmaxalgolpoly(A)

Author

"Max-Plus Algebra Toolbox", ver. 1.1.0, March, 2012.

See Also


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