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MaxPlusAndPetrinet >> MaxPlusAndPetrinet > maxplusmaxalgolgeneral

maxplusmaxalgolgeneral

Max-plus algebra generalization eigenvalue and eigenvector

Calling Sequence

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

Parameters

A
: a square input matrix.
l
: an eigenvalue of the matrix A.
v
: a corresponding eigenvector of the matrix A .
d

: a row vector which form of d is [q,\sigma, r,1]

Description

The function valid for both an irreducible and a reducible matrix A, and returns eigenvector and a 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 .

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

Examples

A = [12. -%inf -%inf  19. 13.  5.  15. -%inf -%inf -%inf;   
     11.  10.   16.    9. -%inf  13.  6.  8.  5. 18.;  
     -%inf  8. -%inf -%inf  19. -%inf  8. -%inf  4. -%inf;   
     17. -%inf  16. -%inf  -%inf  5. -%inf 17. 16. 19.;  
     -%inf -%inf 4. -%inf  8. -%inf  20. -%inf  16. 14.;  
     6.  2. 7. -%inf -%inf -%inf -%inf -%inf 10. 19.;  
     -%inf 1. -%inf -%inf 9. -%inf 14. 5. -%inf 1.;   
     19. -%inf 9. 19. 4. 20. 18. 10. 16. 11.;  
     5. -%inf 13. 15. -%inf -%inf -%inf 20. 3. -%inf;   
     18.  15. -%inf -%inf 7. -%inf 13. 9. 15. 6.];
[l,v,d]=maxplusmaxalgolgeneral(A)

e=-%inf;
B=[e e 16 e e e e e e e;   
     14 15 18 e e e e e e e;  
     14 2 e 1 e e e e e e;   
     17 3 e 12 2 e 3 e e e;  
     12 e e 1 e e e e e e;  
     e e e e e 8 e e e e;  
     e e e e e e 7 19 e e;   
     e e e e e e e e 2 e;  
     e e e e e e e 13 e e;   
     e e e e e 10 7 12 2 5];
[l,v,d]=maxplusmaxalgolgeneral(B)

Author

"Max-Plus Algebra Toolbox", ver. 1.1.0, Mei, 2015.

See Also


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