Iterative methods: problems with Gauss-Seidel and Gauss-Jacobi

[ivan.zapreev]

See test:

test/functional_tests/ctmc/csl/operators/steady_state/csl_steady_state_03

When checking

S{>0.1}[ a5 ]

(Gauss-Seidel) steady state probabilities differ in ETMCC 1.0, PRISM 2.1 and MRMC :

  ETMCC 1.0:
    SSGaussSeidelPred: Result:  0.0 0.0 0.0 0.0 0.5714285714285714 0.2857142857142857 0.14285714285714285
  
  PRISM 2.1:
    ( 0.0 0.0 0.0 0.0 0.4 0.4 0.2 )
    
  MRMC 1.0 alpha:
    ( 0.0e+00, 0.0e+00, 0.0e+00, 0.0e+00, 4.000000000000000e-01, 4.000000000000000e-01, 2.000000000000000e-01 )

Also, in test

test/functional_tests/ctmc/csl/operators/steady_state/csl_steady_state_02

the steady-state probabilities for

S{>0.1}[ a5 ] and S{>0.1}[ a6 ]

are interchanged comparing to ETMCC 1.0 and PRISM 2.1. It is strange but steady state probabilities computed with Gauss-Seidel and Gauss-Jacobi interchange in ETMCC 1.0 and PRISM 2.1! In our implementation we have smth like in PRISM 2.1.

[ivan.zapreev]

Here the problem is that Inverted Jacobi does not converge having initial vector & matrix:

(1/3,1/3,1/3),  |-1  1  0|
                | 0 -1  1| 
                | 2  0 -2|

iterations give:

0: (1/3,1/3,1/3)
1: (2/3,1/3,1/6)
2: (1/3,2/3,1/6)
3: (1/3,1/3,1/3)
4:     ....

So depending on what iteration we stop we have alternation for 1 & 2 state probabilities: 1/3 and 2/3.