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 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.distribution;

import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.Pair;

Class for representing 
mixture model distributions.
Type parameters:
<T> – Type of the mixture components.
Since:
3.1/**
 * Class for representing <a href="http://en.wikipedia.org/wiki/Mixture_model">
 * mixture model</a> distributions.
 *
 * @param <T> Type of the mixture components.
 *
 * @since 3.1
 */
public class MixtureMultivariateRealDistribution<T extends MultivariateRealDistribution>
    extends AbstractMultivariateRealDistribution {
    
Normalized weight of each mixture component. /** Normalized weight of each mixture component. */
    private final double[] weight;
    
Mixture components. /** Mixture components. */
    private final List<T> distribution;

    
Creates a mixture model from a list of distributions and their
associated weights.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractMultivariateRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead. 
Params:
components – List of (weight, distribution) pairs from which to sample./**
     * Creates a mixture model from a list of distributions and their
     * associated weights.
     * <p>
     * <b>Note:</b> this constructor will implicitly create an instance of
     * {@link Well19937c} as random generator to be used for sampling only (see
     * {@link #sample()} and {@link #sample(int)}). In case no sampling is
     * needed for the created distribution, it is advised to pass {@code null}
     * as random generator via the appropriate constructors to avoid the
     * additional initialisation overhead.
     *
     * @param components List of (weight, distribution) pairs from which to sample.
     */
    public MixtureMultivariateRealDistribution(List<Pair<Double, T>> components) {
        this(new Well19937c(), components);
    }

    
Creates a mixture model from a list of distributions and their
associated weights.
Params:
rng – Random number generator.
components – Distributions from which to sample.
Throws:
NotPositiveException – if any of the weights is negative.
DimensionMismatchException – if not all components have the same
number of variables./**
     * Creates a mixture model from a list of distributions and their
     * associated weights.
     *
     * @param rng Random number generator.
     * @param components Distributions from which to sample.
     * @throws NotPositiveException if any of the weights is negative.
     * @throws DimensionMismatchException if not all components have the same
     * number of variables.
     */
    public MixtureMultivariateRealDistribution(RandomGenerator rng,
                                               List<Pair<Double, T>> components) {
        super(rng, components.get(0).getSecond().getDimension());

        final int numComp = components.size();
        final int dim = getDimension();
        double weightSum = 0;
        for (int i = 0; i < numComp; i++) {
            final Pair<Double, T> comp = components.get(i);
            if (comp.getSecond().getDimension() != dim) {
                throw new DimensionMismatchException(comp.getSecond().getDimension(), dim);
            }
            if (comp.getFirst() < 0) {
                throw new NotPositiveException(comp.getFirst());
            }
            weightSum += comp.getFirst();
        }

        // Check for overflow.
        if (Double.isInfinite(weightSum)) {
            throw new MathArithmeticException(LocalizedFormats.OVERFLOW);
        }

        // Store each distribution and its normalized weight.
        distribution = new ArrayList<T>();
        weight = new double[numComp];
        for (int i = 0; i < numComp; i++) {
            final Pair<Double, T> comp = components.get(i);
            weight[i] = comp.getFirst() / weightSum;
            distribution.add(comp.getSecond());
        }
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double density(final double[] values) {
        double p = 0;
        for (int i = 0; i < weight.length; i++) {
            p += weight[i] * distribution.get(i).density(values);
        }
        return p;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    public double[] sample() {
        // Sampled values.
        double[] vals = null;

        // Determine which component to sample from.
        final double randomValue = random.nextDouble();
        double sum = 0;

        for (int i = 0; i < weight.length; i++) {
            sum += weight[i];
            if (randomValue <= sum) {
                // pick model i
                vals = distribution.get(i).sample();
                break;
            }
        }

        if (vals == null) {
            // This should never happen, but it ensures we won't return a null in
            // case the loop above has some floating point inequality problem on
            // the final iteration.
            vals = distribution.get(weight.length - 1).sample();
        }

        return vals;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    public void reseedRandomGenerator(long seed) {
        // Seed needs to be propagated to underlying components
        // in order to maintain consistency between runs.
        super.reseedRandomGenerator(seed);

        for (int i = 0; i < distribution.size(); i++) {
            // Make each component's seed different in order to avoid
            // using the same sequence of random numbers.
            distribution.get(i).reseedRandomGenerator(i + 1 + seed);
        }
    }

    
Gets the distributions that make up the mixture model.
Returns:
the component distributions and associated weights./**
     * Gets the distributions that make up the mixture model.
     *
     * @return the component distributions and associated weights.
     */
    public List<Pair<Double, T>> getComponents() {
        final List<Pair<Double, T>> list = new ArrayList<Pair<Double, T>>(weight.length);

        for (int i = 0; i < weight.length; i++) {
            list.add(new Pair<Double, T>(weight[i], distribution.get(i)));
        }

        return list;
    }
}