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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