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MaxPlusAndPetrinet >> MaxPlusAndPetrinet > maxplusaplus

maxplusaplus

Max-plus algebra Aλ+

Calling Sequence

[ap,lam] = maxplusaplus(A)

Parameters

A
: an input matrix of size n × n.
ap

:is an output matrix of size as the matrix A.

lam

:is an output scalar, this one is an eigenvalue of the matrix A.

Description

The function returns

ap = Aλ⊕ Aλ2 ⊕ Aλ3⊕ ⋯ ⊕ Aλn

where Aλ = -λ ⊗ A , with λ is an an eigenvalue of A, and an error if the matrix A does not has a unique eigenvalue.

If x ∊ GC(A) , where GC(A) is critical path of matrix A, then the column x-th of matrix ap is an eigenvector of A

corresponding to eigenvalue lam.

Examples

A=[5 -%inf 5;-%inf 6 3;6 6 3]
[ap,lam]=maxplusaplus(A) 
// We find a critical circuit graph of matrix A
// as follows
[l,d,x] = maxplusccir(A)
// The elemen of x gives information a critical
// circuit graph of matrix A. The critical circuit
// is: 2 ↔ 2 . So vector  v the 2-th column of matrix ap is
// an eigenvector of A corresponding to the eigenvalue lam or l.
// Indeed this true that A ⊗ v = lam ⊗ v
isequal(maxplusotimes(A,ap(:,2)),maxplusotimes(lam,ap(:,2)))

Author

"Max-Plus Algebra And Petrinet Toolbox", ver. 1.1.0, February, 2013.

See Also


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