package de.ugoe.cs.quest.usageprofiles;

import java.util.ArrayList;
import java.util.Collection;
import java.util.LinkedList;
import java.util.List;
import java.util.Random;

import de.ugoe.cs.quest.eventcore.Event;
import de.ugoe.cs.util.StringTools;
import de.ugoe.cs.util.console.Console;
import edu.uci.ics.jung.graph.Graph;
import edu.uci.ics.jung.graph.SparseMultigraph;
import edu.uci.ics.jung.graph.util.EdgeType;

import Jama.Matrix;

/**
 * <p>
 * Implements first-order Markov models. The implementation is based on
 * {@link HighOrderMarkovModel} and restricts the Markov order to 1. In
 * comparison to {@link HighOrderMarkovModel}, more calculations are possible
 * with first-order models, e.g., the calculation of the entropy (
 * {@link #calcEntropy()}).
 * </p>
 * 
 * @author Steffen Herbold
 * @version 1.0
 */
public class FirstOrderMarkovModel extends HighOrderMarkovModel implements
		IDotCompatible {

	/**
	 * <p>
	 * Id for object serialization.
	 * </p>
	 */
	private static final long serialVersionUID = 1L;

	/**
	 * <p>
	 * Maximum number of iterations when calculating the stationary distribution
	 * as the limit of multiplying the transmission matrix with itself.
	 * </p>
	 */
	final static int MAX_STATDIST_ITERATIONS = 1000;

	/**
	 * <p>
	 * Constructor. Creates a new FirstOrderMarkovModel.
	 * </p>
	 * 
	 * @param r
	 *            random number generator used by probabilistic methods of the
	 *            class
	 */
	public FirstOrderMarkovModel(Random r) {
		super(1, r);
	}

	/**
	 * <p>
	 * Generates the transmission matrix of the Markov model.
	 * </p>
	 * 
	 * @return transmission matrix
	 */
	private Matrix getTransmissionMatrix() {
		List<Event<?>> knownSymbols = new ArrayList<Event<?>>(
				trie.getKnownSymbols());
		int numStates = knownSymbols.size();
		Matrix transmissionMatrix = new Matrix(numStates, numStates);

		for (int i = 0; i < numStates; i++) {
			Event<?> currentSymbol = knownSymbols.get(i);
			List<Event<?>> context = new ArrayList<Event<?>>();
			context.add(currentSymbol);
			for (int j = 0; j < numStates; j++) {
				Event<?> follower = knownSymbols.get(j);
				double prob = getProbability(context, follower);
				transmissionMatrix.set(i, j, prob);
			}
		}
		return transmissionMatrix;
	}

	/**
	 * <p>
	 * Calculates the entropy of the model. To make it possible that the model
	 * is stationary, a transition from {@link Event#ENDEVENT} to
	 * {@link Event#STARTEVENT} is added.
	 * </p>
	 * 
	 * @return entropy of the model or NaN if it could not be calculated
	 */
	public double calcEntropy() {
		Matrix transmissionMatrix = getTransmissionMatrix();
		List<Event<?>> knownSymbols = new ArrayList<Event<?>>(
				trie.getKnownSymbols());
		int numStates = knownSymbols.size();

		List<Integer> startIndexList = new LinkedList<Integer>();
		List<Integer> endIndexList = new LinkedList<Integer>();
		for( int i=0 ; i<knownSymbols.size() ; i++ ) {
			String id = knownSymbols.get(i).getStandardId();
			if( id.equals(Event.STARTEVENT.getStandardId()) || id.contains(Event.STARTEVENT.getStandardId()+"-=-") ) {
				startIndexList.add(i);
			}
			if( id.equals(Event.ENDEVENT.getStandardId()) || id.contains("-=-"+Event.ENDEVENT.getStandardId()) ) {
				endIndexList.add(i);
			}
		}
		
		if (startIndexList.isEmpty()) {	
			Console.printerrln("Error calculating entropy. Initial state of markov chain not found.");
			return Double.NaN;
		}
		if (endIndexList.isEmpty()) {
			Console.printerrln("Error calculating entropy. End state of markov chain not found.");
			return Double.NaN;
		}
		for( Integer i : endIndexList ) {
			for(Integer j : startIndexList ) {
				transmissionMatrix.set(i, j, 1);
			}
		}

		// Calculate stationary distribution by raising the power of the
		// transmission matrix.
		// The rank of the matrix should fall to 1 and each two should be the
		// vector of the stationory distribution.
		int iter = 0;
		int rank = transmissionMatrix.rank();
		Matrix stationaryMatrix = (Matrix) transmissionMatrix.clone();
		while (iter < MAX_STATDIST_ITERATIONS && rank > 1) {
			stationaryMatrix = stationaryMatrix.times(stationaryMatrix);
			rank = stationaryMatrix.rank();
			iter++;
		}

		if (rank != 1) {
			Console.traceln("rank: " + rank);
			Console.printerrln("Unable to calculate stationary distribution.");
			return Double.NaN;
		}

		double entropy = 0.0;
		for (int i = 0; i < numStates; i++) {
			for (int j = 0; j < numStates; j++) {
				if (transmissionMatrix.get(i, j) != 0 && transmissionMatrix.get(i, j)!=1) {
					double tmp = stationaryMatrix.get(0, i);
					tmp *= transmissionMatrix.get(i, j);
					tmp *= Math.log(transmissionMatrix.get(i, j)) / Math.log(2);
					entropy -= tmp;
				}
			}
		}
		return entropy;
	}

	/**
	 * <p>
	 * The dot represenation of {@link FirstOrderMarkovModel}s is its graph
	 * representation with the states as nodes and directed edges weighted with
	 * transition probabilities.
	 * </p>
	 * 
	 * @see de.ugoe.cs.quest.usageprofiles.IDotCompatible#getDotRepresentation()
	 */
	@Override
	public String getDotRepresentation() {
		StringBuilder stringBuilder = new StringBuilder();
		stringBuilder.append("digraph model {" + StringTools.ENDLINE);

		List<Event<?>> knownSymbols = new ArrayList<Event<?>>(
				trie.getKnownSymbols());
		for (Event<?> symbol : knownSymbols) {
			final String thisSaneId = symbol.getShortId().replace("\"", "\\\"")
					.replaceAll("[\r\n]", "");
			stringBuilder.append(" " + knownSymbols.indexOf(symbol) + " [label=\""
					+ thisSaneId + "\"];" + StringTools.ENDLINE);
			List<Event<?>> context = new ArrayList<Event<?>>();
			context.add(symbol);
			Collection<Event<?>> followers = trie.getFollowingSymbols(context);
			for (Event<?> follower : followers) {
				stringBuilder.append(" " + knownSymbols.indexOf(symbol) + " -> "
						+ knownSymbols.indexOf(follower) + " ");
				stringBuilder.append("[label=\""
						+ getProbability(context, follower) + "\"];"
						+ StringTools.ENDLINE);
			}
		}
		stringBuilder.append('}' + StringTools.ENDLINE);
		return stringBuilder.toString();
	}

	/**
	 * <p>
	 * Returns a {@link Graph} representation of the model with the states as
	 * nodes and directed edges weighted with transition probabilities.
	 * </p>
	 * 
	 * @return {@link Graph} of the model
	 */
	public Graph<String, MarkovEdge> getGraph() {
		Graph<String, MarkovEdge> graph = new SparseMultigraph<String, MarkovEdge>();

		List<Event<?>> knownSymbols = new ArrayList<Event<?>>(
				trie.getKnownSymbols());

		for (Event<?> symbol : knownSymbols) {
			String from = symbol.getShortId();
			List<Event<?>> context = new ArrayList<Event<?>>();
			context.add(symbol);

			Collection<Event<?>> followers = trie.getFollowingSymbols(context);

			for (Event<?> follower : followers) {
				String to = follower.getShortId();
				MarkovEdge prob = new MarkovEdge(getProbability(context,
						follower));
				graph.addEdge(prob, from, to, EdgeType.DIRECTED);
			}
		}
		return graph;
	}

	/**
	 * Inner class used for the {@link Graph} representation of the model.
	 * 
	 * @author Steffen Herbold
	 * @version 1.0
	 */
	static public class MarkovEdge {
		/**
		 * <p>
		 * Weight of the edge, i.e., its transition probability.
		 * </p>
		 */
		double weight;

		/**
		 * <p>
		 * Constructor. Creates a new MarkovEdge.
		 * </p>
		 * 
		 * @param weight
		 *            weight of the edge, i.e., its transition probability
		 */
		MarkovEdge(double weight) {
			this.weight = weight;
		}

		/**
		 * <p>
		 * The weight of the edge as {@link String}.
		 * </p>
		 */
		public String toString() {
			return "" + weight;
		}
	}

}
