maxplusmaxalgol

A =[-%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];
// check strognly connected (irreducible) of A
s=maxplusscg(A)
s  =
 
  T  

[l,v,d] = maxplusmaxalgol(A)
 d  =
 
    1.  
 v  =
 
    15.  
    15.  
    17.  
    10.  
    16.  
    13.  
 l  =
 
    8.  

// check v is the eigenvector of A with corresponding eigenvalue l
 z  = maxplusisegv(A,v,l) 
 z  =
 
  T  

// or we can check as follows :
isequal(maxplusotimes(A,v),maxplusotimes(l,v))
 ans  =
 
  T  

// instead of we can use maxalgol
[l,v,d] = maxalgol(A)
 d  =
 
    1.  
 v  =
 
    15.  
    15.  
    17.  
    10.  
    16.  
    13.  
 l  =
 
    8. 
// Example reducible matrix
 
 A=[7 -%inf;0 3]
 A  =
 
    7.  -Inf  
    0.    3.  
 
// Check matrix A is not irreducible
 
 s=maxplusscg(A)
 s  =
 
  F  
 
[l,v,d] = maxplusmaxalgol(A)
 d  =
 
    1.  
 v  =
 
    14.  
    7.   
 l  =
 
    7.  

// check v is the eigenvector of A with the eigenvalue l
 
 z = maxplusisegv(A,v,l)
 z  =
 
  T
// Example reducible matrix but the cycle time vector at least contain two
// difference elements, and returns an error massage.
 A=[8 -%inf;0 11]
 A  =
 
    8.  -Inf   
    0.    11.  
// check cycle time vector of matix A and, run maxplusmaxalgol
s=maxplusctv(A)
 s  =
 
    8.   
    11. // the cycle time vector contains difference elements 

[l,v,d]=maxplusmaxalgol(A)
 !--error 10000 
The matrix does not has a unique eigenvalue
at line      32 of function called by :  
[l,v]=maxplusmaxalgol(A)

// Example if numerical error exists                    

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]=maxplusmaxalgol(A);

// this means that, the maxplusmaxalgol still work, returns A⊗v ≠ l⊗v,
// but the norm of (A⊗v-l⊗v)≤4.019D-14

~isequal(maxplusotimes(A,v),maxplusotimes(l,v))
 ans  =
 
  T // this is true that A⊗v ≠ l⊗v and the norm given by

norm(maxplusotimes(a,v)-maxplusotimes(l,v))
 ans  =
 
    4.019D-14