[1] | 1 | package de.ugoe.cs.eventbench.markov;
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| 2 |
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| 3 | import java.util.ArrayList;
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| 4 | import java.util.LinkedList;
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| 5 | import java.util.List;
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| 6 | import java.util.Random;
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| 7 |
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| 8 | import Jama.Matrix;
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| 9 |
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| 10 | import de.ugoe.cs.eventbench.data.Event;
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| 11 | import de.ugoe.cs.util.console.Console;
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| 12 | import edu.uci.ics.jung.graph.Graph;
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| 13 | import edu.uci.ics.jung.graph.SparseMultigraph;
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| 14 | import edu.uci.ics.jung.graph.util.EdgeType;
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| 15 |
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| 16 | public class MarkovModel implements DotPrinter {
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| 17 |
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| 18 | private State initialState;
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| 19 | private State endState;
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| 20 |
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| 21 | private List<State> states;
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| 22 | private List<String> stateIdList;
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| 23 |
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| 24 | private Random r;
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| 25 |
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| 26 | final static int MAX_STATDIST_ITERATIONS = 1000;
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| 27 |
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| 28 | /**
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| 29 | * <p>
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| 30 | * Default constructor. Creates a new random number generator.
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| 31 | * </p>
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| 32 | */
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| 33 | public MarkovModel() {
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| 34 | this(new Random());
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| 35 | }
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| 36 |
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| 37 | /**
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| 38 | * <p>
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| 39 | * Creates a new {@link MarkovModel} with a predefined random number generator.
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| 40 | * </p>
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| 41 | *
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| 42 | * @param r random number generator
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| 43 | */
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| 44 | public MarkovModel(Random r) {
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| 45 | this.r = r; // defensive copy would be better, but constructor Random(r) does not seem to exist.
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| 46 | }
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| 47 |
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| 48 | public void printRandomWalk() {
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| 49 | State currentState = initialState;
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| 50 | IMemory<State> history = new IncompleteMemory<State>(5); // this is NOT used here, just for testing ...
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| 51 | history.add(currentState);
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| 52 | Console.println(currentState.getId());
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| 53 | while(!currentState.equals(endState)) {
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| 54 | currentState = currentState.getNextState();
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| 55 | Console.println(currentState.getId());
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| 56 | history.add(currentState);
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| 57 | }
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| 58 | }
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| 59 |
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| 60 | public List<? extends Event<?>> randomSequence() {
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| 61 | List<Event<?>> sequence = new LinkedList<Event<?>>();
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| 62 | State currentState = initialState;
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| 63 | if( currentState.getAction()!=null ) {
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| 64 | sequence.add(currentState.getAction());
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| 65 | }
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| 66 | System.out.println(currentState.getId());
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| 67 | while(!currentState.equals(endState)) {
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| 68 | currentState = currentState.getNextState();
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| 69 | if( currentState.getAction()!=null ) {
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| 70 | sequence.add(currentState.getAction());
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| 71 | }
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| 72 | System.out.println(currentState.getId());
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| 73 | }
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| 74 | return sequence;
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| 75 | }
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| 76 |
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| 77 | public void printDot() {
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| 78 | int numUnprintableStates = 0;
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| 79 | System.out.println("digraph model {");
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| 80 | for( State state : states ) {
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| 81 | if( state instanceof DotPrinter ) {
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| 82 | ((DotPrinter) state).printDot();
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| 83 | } else {
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| 84 | numUnprintableStates++;
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| 85 | }
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| 86 | }
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| 87 | System.out.println('}');
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| 88 | if( numUnprintableStates>0 ) {
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| 89 | Console.println("" + numUnprintableStates + "/" + states.size() + "were unprintable!");
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| 90 | }
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| 91 | }
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| 92 |
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| 93 | public Graph<String, MarkovEdge> getGraph() {
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| 94 | Graph<String, MarkovEdge> graph = new SparseMultigraph<String, MarkovEdge>();
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| 95 |
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| 96 | for( State state : states) {
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| 97 | try {
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| 98 | SimpleState simpleState = (SimpleState) state;
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| 99 | String from = simpleState.getShortId();
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| 100 | for( int i=0 ; i<simpleState.toStates.size() ; i++ ) {
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| 101 | SimpleState toState = (SimpleState) simpleState.toStates.get(i);
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| 102 | String to = toState.getShortId();
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| 103 | MarkovEdge prob = new MarkovEdge(simpleState.transitionProbs.get(i));
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| 104 | graph.addEdge(prob, from, to, EdgeType.DIRECTED);
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| 105 | }
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| 106 | } catch (ClassCastException e) {
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| 107 | // TODO: handle exception
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| 108 | }
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| 109 | }
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| 110 |
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| 111 | return graph;
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| 112 | }
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| 113 |
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| 114 | static public class MarkovEdge {
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| 115 | double weight;
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| 116 | MarkovEdge(double weight) { this.weight = weight; }
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| 117 | public String toString() { return ""+weight; }
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| 118 | }
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| 119 |
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| 120 | /////////////////////////////////////////////////////////////////////////////////////
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| 121 | // Code to learn type1 model: states are wndid.action and transitions are unlabled //
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| 122 | /////////////////////////////////////////////////////////////////////////////////////
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| 123 |
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| 124 | public void train(List<List<Event<?>>> sequences) {
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| 125 | Event<?> fromElement = null;
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| 126 | Event<?> toElement = null;
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| 127 | SimpleState fromState;
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| 128 | SimpleState toState;
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| 129 |
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| 130 | states = new ArrayList<State>();
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| 131 | stateIdList = new ArrayList<String>();
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| 132 | initialState = new SimpleState("GLOBALSTARTSTATE", null);
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| 133 | initialState.setRandom(r);
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| 134 | states.add(initialState);
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| 135 | stateIdList.add("GLOBALSTARTSTATE");
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| 136 | endState = new SimpleState("GLOBALENDSTATE", null);
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| 137 | endState.setRandom(r);
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| 138 | states.add(endState);
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| 139 | stateIdList.add("GLOBALENDSTATE");
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| 140 | for( List<Event<?>> sequence : sequences ) {
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| 141 | for( int i=0; i<sequence.size() ; i++ ) {
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| 142 | if( i==0 ) {
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| 143 | fromState = (SimpleState) initialState;
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| 144 | } else {
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| 145 | fromElement = sequence.get(i-1);
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| 146 | fromState = findOrCreateSimpleState(fromElement);
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| 147 | }
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| 148 |
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| 149 | toElement = sequence.get(i);
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| 150 | toState = findOrCreateSimpleState(toElement);
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| 151 |
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| 152 | fromState.incTransTo(toState);
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| 153 |
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| 154 | if( i==sequence.size()-1 ) {
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| 155 | toState.incTransTo(endState);
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| 156 | }
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| 157 | }
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| 158 | }
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| 159 | }
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| 160 |
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| 161 | private SimpleState findOrCreateSimpleState(Event<?> action) {
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| 162 | SimpleState state = null;
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| 163 | String id = action.getStandardId();
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| 164 | String idShort = action.getShortId();
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| 165 | int index = stateIdList.indexOf(id);
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| 166 | if( index!=-1 ) {
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| 167 | state = (SimpleState) states.get(index);
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| 168 | } else {
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| 169 | state = new SimpleState(id, action, idShort);
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| 170 | state.setRandom(r);
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| 171 | states.add(state);
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| 172 | stateIdList.add(id);
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| 173 | }
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| 174 | return state;
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| 175 | }
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| 176 |
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| 177 | ///////////////////////////////////////////////////////////
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| 178 |
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| 179 | // states must be SimpleState, this functions will throw bad cast exceptions
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| 180 | public double calcEntropy() {
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| 181 | int numStates = states.size();
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| 182 | // create transmission matrix
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| 183 | Matrix transmissionMatrix = new Matrix(numStates, numStates);
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| 184 | for( int i=0 ; i<numStates ; i++ ) {
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| 185 | State tmpState = states.get(i);
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| 186 | if( SimpleState.class.isInstance(tmpState) ) {
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| 187 | SimpleState currentState = (SimpleState) tmpState;
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| 188 | for( int j=0 ; j<numStates ; j++ ) {
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| 189 | double prob = currentState.getProb(states.get(j));
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| 190 | transmissionMatrix.set(i, j, prob);
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| 191 | }
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| 192 | } else {
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| 193 | Console.printerr("Error calculating entropy. Only allowed for first-order markov models.");
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| 194 | return Double.NaN;
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| 195 | }
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| 196 | }
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| 197 |
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| 198 | // Add transition from endState to startState. This makes the markov chain irreducible and recurrent.
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| 199 | int startStateIndex = states.indexOf(initialState);
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| 200 | int endStateIndex = states.indexOf(endState);
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| 201 | if( startStateIndex==-1 ) {
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| 202 | Console.printerrln("Error calculating entropy. Initial state of markov chain not found.");
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| 203 | return Double.NaN;
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| 204 | }
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| 205 | if( endStateIndex==-1 ) {
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| 206 | Console.printerrln("Error calculating entropy. End state of markov chain not found.");
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| 207 | return Double.NaN;
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| 208 | }
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| 209 | transmissionMatrix.set(endStateIndex, startStateIndex, 1);
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| 210 |
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| 211 | // Calculate stationary distribution by raising the power of the transmission matrix.
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| 212 | // The rank of the matrix should fall to 1 and each two should be the vector of the
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| 213 | // stationory distribution.
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| 214 | int iter = 0;
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| 215 | int rank = transmissionMatrix.rank();
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| 216 | Matrix stationaryMatrix = (Matrix) transmissionMatrix.clone();
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| 217 | while( iter<MAX_STATDIST_ITERATIONS && rank>1 ) {
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| 218 | stationaryMatrix = stationaryMatrix.times(stationaryMatrix);
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| 219 | rank = stationaryMatrix.rank();
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| 220 | iter++;
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| 221 | }
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| 222 |
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| 223 | if( rank!=1 ) {
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| 224 | Console.traceln("rank: " + rank);
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| 225 | Console.printerrln("Unable to calculate stationary distribution.");
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| 226 | return Double.NaN;
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| 227 | }
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| 228 |
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| 229 | double entropy = 0.0;
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| 230 | for( int i=0 ; i<numStates ; i++ ) {
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| 231 | for( int j=0 ; j<numStates ; j++ ) {
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| 232 | if( transmissionMatrix.get(i,j)!=0 ) {
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| 233 | double tmp = stationaryMatrix.get(i, 0);
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| 234 | tmp *= transmissionMatrix.get(i, j);
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| 235 | tmp *= Math.log(transmissionMatrix.get(i,j))/Math.log(2);
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| 236 | entropy -= tmp;
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| 237 | }
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| 238 | }
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| 239 | }
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| 240 | return entropy;
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| 241 | }
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| 242 | }
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