/*******************************************************************************
*   Copyright 2013 Analog Devices, Inc.
*
*   Licensed under the Apache License, Version 2.0 (the "License");
*   you may not use this file except in compliance with the License.
*   You may obtain a copy of the License at
*
*       http://www.apache.org/licenses/LICENSE-2.0
*
*   Unless required by applicable law or agreed to in writing, software
*   distributed under the License is distributed on an "AS IS" BASIS,
*   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*   See the License for the specific language governing permissions and
*   limitations under the License.
********************************************************************************/

package com.analog.lyric.dimple.factorfunctions;

import com.analog.lyric.dimple.exceptions.DimpleException;
import com.analog.lyric.dimple.factorfunctions.core.FactorFunction;
import com.analog.lyric.dimple.factorfunctions.core.FactorFunctionUtilities;
import com.analog.lyric.dimple.model.values.Value;


/**
 * Parameterized multinomial distribution, which corresponds to p(x | N, alpha),
 * where x is a vector of discrete count variables, N is the total count across all categories, and
 * where alpha is a RealJoint variable vector of (not necessarily normalized) probabilities.
 * <p>
 * The domain of each x variable must be a zero-based integer with maximum value N (domain 0 through N).
 * If N is a variable rather than a constant, then the domain of each x must be range from 0 through
 * the maximum value in the domain of N.
 * <p>
 * Representing alpha as described, the conjugate prior for alpha is
 * a Dirichlet distribution.
 * Depending on the solver, it may or may not be necessary to use a
 * conjugate prior (for the Gibbs solver, for example, it is not).
 * <p>
 * The variables in the argument list are ordered as follows:
 * <ol>
 * <li> N: Parameter indicating the total count
 * <li> Alpha: RealJoint variable containing probabilities
 * <li> ... x: A number of discrete count variable, where the number of variables
 *    must equal the dimension of alpha
 * </ol>
 * N parameter may optionally be specified as a constant in the constructor.
 * In this case, N is not included in the list of arguments.
 * 
 * @since 0.06
 */
public class Multinomial extends FactorFunction
{
	protected int _N;
	protected double _negativeLogFactorialN;
	protected boolean _NParameterConstant = false;
	private int _firstDirectedToIndex = 2;

	
	public Multinomial() {super();}		// Variable N
	public Multinomial(int N)			// Fixed N
	{
		this();
		_N = N;
    	if (_N < 0) throw new DimpleException("N must be a non-negative value.");
		_negativeLogFactorialN = -org.apache.commons.math3.special.Gamma.logGamma(_N + 1);
		_NParameterConstant = true;
		_firstDirectedToIndex = 1;
	}

    @Override
	public final double evalEnergy(Value[] arguments)
    {
    	int index = 0;
    	if (!_NParameterConstant)
    	{
    		_N = arguments[index++].getInt();	// First argument is N parameter
    		if (_N < 0) return Double.POSITIVE_INFINITY;
    		_negativeLogFactorialN = -org.apache.commons.math3.special.Gamma.logGamma(_N + 1);
    	}
    	
    	final double[] alpha = arguments[index++].getDoubleArray();		// Next argument is the probability parameter vector
    	final int dimension = alpha.length;
    	
    	if (arguments.length - index != dimension)
    		throw new DimpleException("Number of count variables must equal the dimension of the parameter vector.");


    	int countSum = 0;
    	double parameterSum = 0;
    	double sum = _negativeLogFactorialN;
    	for (int i = 0; i < dimension; i++)
    	{
    		final double alphai = alpha[i];
    		if (alphai < 0)
    			return Double.POSITIVE_INFINITY;
    		parameterSum += alphai;

    		final int x = arguments[index++].getInt();					// Remaining arguments are discrete count variables
    		if (x < 0)
    			return Double.POSITIVE_INFINITY;
    		countSum += x;
    		
    		double negativeXLogAlphai;
    		if (alphai == 0 && x == 0)
    			negativeXLogAlphai = 0;
    		else
    			negativeXLogAlphai = -x * Math.log(alphai);
    		sum += negativeXLogAlphai + org.apache.commons.math3.special.Gamma.logGamma(x + 1);
    	}
    	if (countSum != _N)
			return Double.POSITIVE_INFINITY;

    	final double energy = sum + _N * Math.log(parameterSum);
    	if (energy != energy)	// Faster isNaN
    		return Double.POSITIVE_INFINITY;
    	
    	return energy;
	}
    
    @Override
    public final boolean isDirected() {return true;}
    @Override
	public final int[] getDirectedToIndices(int numEdges)
	{
    	// All edges except the parameter edges (if present) are directed-to edges
		return FactorFunctionUtilities.getListOfIndices(_firstDirectedToIndex, numEdges-1);
	}
    
    
    // Factor-specific methods
    public final boolean hasConstantNParameter()
    {
    	return _NParameterConstant;
    }
    public final int getN()
    {
    	return _N;
    }
}