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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
 *
 *      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
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package org.apache.commons.math3.distribution;

import java.io.Serializable;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NotANumberException;
import org.apache.commons.math3.exception.NotFiniteNumberException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
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.MathArrays;
import org.apache.commons.math3.util.Pair;

/**
 * 

A generic implementation of a * * discrete probability distribution (Wikipedia) over a finite sample space, * based on an enumerated list of <value, probability> pairs. Input probabilities must all be non-negative, * but zero values are allowed and their sum does not have to equal one. Constructors will normalize input * probabilities to make them sum to one.

* *

The list of pairs does not, strictly speaking, have to be a function and it can * contain null values. The pmf created by the constructor will combine probabilities of equal values and * will treat null values as equal. For example, if the list of pairs <"dog", 0.2>, <null, 0.1>, * <"pig", 0.2>, <"dog", 0.1>, <null, 0.4> is provided to the constructor, the resulting * pmf will assign mass of 0.5 to null, 0.3 to "dog" and 0.2 to null.

* * @param type of the elements in the sample space. * @since 3.2 */ public class EnumeratedDistribution implements Serializable { /** Serializable UID. */ private static final long serialVersionUID = 20123308L; /** * RNG instance used to generate samples from the distribution. */ protected final RandomGenerator random; /** * List of random variable values. */ private final List singletons; /** * Probabilities of respective random variable values. For i = 0, ..., singletons.size() - 1, * probability[i] is the probability that a random variable following this distribution takes * the value singletons[i]. */ private final double[] probabilities; /** * Cumulative probabilities, cached to speed up sampling. */ private final double[] cumulativeProbabilities; /** * Create an enumerated distribution using the given probability mass function * enumeration. *

* Note: 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 pmf probability mass function enumerated as a list of * pairs. * @throws NotPositiveException if any of the probabilities are negative. * @throws NotFiniteNumberException if any of the probabilities are infinite. * @throws NotANumberException if any of the probabilities are NaN. * @throws MathArithmeticException all of the probabilities are 0. */ public EnumeratedDistribution(final List> pmf) throws NotPositiveException, MathArithmeticException, NotFiniteNumberException, NotANumberException { this(new Well19937c(), pmf); } /** * Create an enumerated distribution using the given random number generator * and probability mass function enumeration. * * @param rng random number generator. * @param pmf probability mass function enumerated as a list of * pairs. * @throws NotPositiveException if any of the probabilities are negative. * @throws NotFiniteNumberException if any of the probabilities are infinite. * @throws NotANumberException if any of the probabilities are NaN. * @throws MathArithmeticException all of the probabilities are 0. */ public EnumeratedDistribution(final RandomGenerator rng, final List> pmf) throws NotPositiveException, MathArithmeticException, NotFiniteNumberException, NotANumberException { random = rng; singletons = new ArrayList(pmf.size()); final double[] probs = new double[pmf.size()]; for (int i = 0; i < pmf.size(); i++) { final Pair sample = pmf.get(i); singletons.add(sample.getKey()); final double p = sample.getValue(); if (p < 0) { throw new NotPositiveException(sample.getValue()); } if (Double.isInfinite(p)) { throw new NotFiniteNumberException(p); } if (Double.isNaN(p)) { throw new NotANumberException(); } probs[i] = p; } probabilities = MathArrays.normalizeArray(probs, 1.0); cumulativeProbabilities = new double[probabilities.length]; double sum = 0; for (int i = 0; i < probabilities.length; i++) { sum += probabilities[i]; cumulativeProbabilities[i] = sum; } } /** * Reseed the random generator used to generate samples. * * @param seed the new seed */ public void reseedRandomGenerator(long seed) { random.setSeed(seed); } /** *

For a random variable {@code X} whose values are distributed according to * this distribution, this method returns {@code P(X = x)}. In other words, * this method represents the probability mass function (PMF) for the * distribution.

* *

Note that if {@code x1} and {@code x2} satisfy {@code x1.equals(x2)}, * or both are null, then {@code probability(x1) = probability(x2)}.

* * @param x the point at which the PMF is evaluated * @return the value of the probability mass function at {@code x} */ double probability(final T x) { double probability = 0; for (int i = 0; i < probabilities.length; i++) { if ((x == null && singletons.get(i) == null) || (x != null && x.equals(singletons.get(i)))) { probability += probabilities[i]; } } return probability; } /** *

Return the probability mass function as a list of pairs.

* *

Note that if duplicate and / or null values were provided to the constructor * when creating this EnumeratedDistribution, the returned list will contain these * values. If duplicates values exist, what is returned will not represent * a pmf (i.e., it is up to the caller to consolidate duplicate mass points).

* * @return the probability mass function. */ public List> getPmf() { final List> samples = new ArrayList>(probabilities.length); for (int i = 0; i < probabilities.length; i++) { samples.add(new Pair(singletons.get(i), probabilities[i])); } return samples; } /** * Generate a random value sampled from this distribution. * * @return a random value. */ public T sample() { final double randomValue = random.nextDouble(); int index = Arrays.binarySearch(cumulativeProbabilities, randomValue); if (index < 0) { index = -index-1; } if (index >= 0 && index < probabilities.length && randomValue < cumulativeProbabilities[index]) { return singletons.get(index); } /* This should never happen, but it ensures we will return a correct * object in case there is some floating point inequality problem * wrt the cumulative probabilities. */ return singletons.get(singletons.size() - 1); } /** * Generate a random sample from the distribution. * * @param sampleSize the number of random values to generate. * @return an array representing the random sample. * @throws NotStrictlyPositiveException if {@code sampleSize} is not * positive. */ public Object[] sample(int sampleSize) throws NotStrictlyPositiveException { if (sampleSize <= 0) { throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize); } final Object[] out = new Object[sampleSize]; for (int i = 0; i < sampleSize; i++) { out[i] = sample(); } return out; } /** * Generate a random sample from the distribution. *

* If the requested samples fit in the specified array, it is returned * therein. Otherwise, a new array is allocated with the runtime type of * the specified array and the size of this collection. * * @param sampleSize the number of random values to generate. * @param array the array to populate. * @return an array representing the random sample. * @throws NotStrictlyPositiveException if {@code sampleSize} is not positive. * @throws NullArgumentException if {@code array} is null */ public T[] sample(int sampleSize, final T[] array) throws NotStrictlyPositiveException { if (sampleSize <= 0) { throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize); } if (array == null) { throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY); } T[] out; if (array.length < sampleSize) { @SuppressWarnings("unchecked") // safe as both are of type T final T[] unchecked = (T[]) Array.newInstance(array.getClass().getComponentType(), sampleSize); out = unchecked; } else { out = array; } for (int i = 0; i < sampleSize; i++) { out[i] = sample(); } return out; } }





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