GitHub - khaledbakeer/MARKOW-Quellen: Eine Markow-Quelle ist das Mathematische Modell einer Informationsquelle, bei dem die aufeinanderfolgende Auswahl von Quellenzeichen, d. h. die Folge der Zustände, sowohl von der momentanen Verteilung der Auftritts- bzw. Zustandswahrscheinlichkeiten als auch von der Verteilung der Übergangswahrscheinlichkeiten abhängt.

Markov chain:

Eine Markow-Quelle ist das Mathematische Modell einer Informationsquelle, bei dem die aufeinanderfolgende Auswahl von Quellenzeichen, d. h. die Folge der Zustände, sowohl von der momentanen Verteilung der Auftritts- bzw. Zustandswahrscheinlichkeiten als auch von der Verteilung der Übergangswahrscheinlichkeiten abhängt.

Example:

        double[] stateProbability = {1, 0, 0, 0};

        double[][] transitionProbability =
                {
                        {0.0, 0.2, 0.7, 0.1},
                        {0.1, 0.6, 0.0, 0.3},
                        {0.2, 0.4, 0.2, 0.2},
                        {0.2, 0.3, 0.1, 0.4}
                };

        Calculate c = new Calculate(transitionProbability, stateProbability);
        c.PrintTransitionProbability();

        System.out.println();

        c.PrintDetailedStateProbability(20);

        c.PrintStateProbabilityTable();

        c.WhenChangedStateProbability();

Output:

Transition Probability: 
-----------------------
0.0 	 0.2 	 0.7 	 0.1 	 
0.1 	 0.6 	 0.0 	 0.3 	 
0.2 	 0.4 	 0.2 	 0.2 	 
0.2 	 0.3 	 0.1 	 0.4 	 


State Probability for t = 0 -> ( 1.0 0.0 0.0 0.0 )
------------------------------------------------
(1.0*0.0) + (0.0*0.1) + (0.0*0.2) + (0.0*0.2) = 0.0

(1.0*0.2) + (0.0*0.6) + (0.0*0.4) + (0.0*0.3) = 0.2

(1.0*0.7) + (0.0*0.0) + (0.0*0.2) + (0.0*0.1) = 0.7

(1.0*0.1) + (0.0*0.3) + (0.0*0.2) + (0.0*0.4) = 0.1


State Probability for t = 1 -> ( 0.0 0.2 0.7 0.1 )
------------------------------------------------
(0.0*0.0) + (0.2*0.1) + (0.7*0.2) + (0.1*0.2) = 0.18

(0.0*0.2) + (0.2*0.6) + (0.7*0.4) + (0.1*0.3) = 0.43

(0.0*0.7) + (0.2*0.0) + (0.7*0.2) + (0.1*0.1) = 0.15

(0.0*0.1) + (0.2*0.3) + (0.7*0.2) + (0.1*0.4) = 0.24


State Probability for t = 2 -> ( 0.18 0.43 0.15 0.24 )
------------------------------------------------
(0.18*0.0) + (0.43*0.1) + (0.15*0.2) + (0.24*0.2) = 0.12

(0.18*0.2) + (0.43*0.6) + (0.15*0.4) + (0.24*0.3) = 0.43

(0.18*0.7) + (0.43*0.0) + (0.15*0.2) + (0.24*0.1) = 0.18

(0.18*0.1) + (0.43*0.3) + (0.15*0.2) + (0.24*0.4) = 0.27


State Probability for t = 3 -> ( 0.12 0.43 0.18 0.27 )
------------------------------------------------
(0.12*0.0) + (0.43*0.1) + (0.18*0.2) + (0.27*0.2) = 0.13

(0.12*0.2) + (0.43*0.6) + (0.18*0.4) + (0.27*0.3) = 0.43

(0.12*0.7) + (0.43*0.0) + (0.18*0.2) + (0.27*0.1) = 0.15

(0.12*0.1) + (0.43*0.3) + (0.18*0.2) + (0.27*0.4) = 0.29


State Probability for t = 4 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 5 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 6 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 7 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 8 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 9 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 10 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 11 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 12 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 13 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 14 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 15 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 16 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 17 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 18 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 19 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


State Probability for t = 20 -> ( 0.13 0.43 0.15 0.29 )
------------------------------------------------
(0.13*0.0) + (0.43*0.1) + (0.15*0.2) + (0.29*0.2) = 0.13

(0.13*0.2) + (0.43*0.6) + (0.15*0.4) + (0.29*0.3) = 0.43

(0.13*0.7) + (0.43*0.0) + (0.15*0.2) + (0.29*0.1) = 0.15

(0.13*0.1) + (0.43*0.3) + (0.15*0.2) + (0.29*0.4) = 0.29


P1 	 1.0 	 0.0 	 0.18 	 0.12 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 0.13 	 
P2 	 0.0 	 0.2 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 0.43 	 
P3 	 0.0 	 0.7 	 0.15 	 0.18 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 0.15 	 
P4 	 0.0 	 0.1 	 0.24 	 0.27 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 0.29 	 
---------------------------------------------------------------------------------
From the t = 6. The State Probability ( 0.13 0.43 0.15 0.29 ) will not change anymore!
---------------------------------------------------------------------------------

Name		Name	Last commit message	Last commit date
Latest commit History 23 Commits
.idea		.idea
src		src
MARKOW-Quellen.iml		MARKOW-Quellen.iml
readme.md		readme.md

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