Java tutorial
/* * 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 * limitations under the License. */ 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; /** * <p>A generic implementation of a * <a href="http://en.wikipedia.org/wiki/Probability_distribution#Discrete_probability_distribution"> * discrete probability distribution (Wikipedia)</a> 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.</p> * * <p>The list of <value, probability> 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.</p> * * @param <T> type of the elements in the sample space. * @since 3.2 */ public class EnumeratedDistribution<T> 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<T> 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. * <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 pmf probability mass function enumerated as a list of <T, probability> * 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<Pair<T, Double>> 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 <T, probability> * 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<Pair<T, Double>> pmf) throws NotPositiveException, MathArithmeticException, NotFiniteNumberException, NotANumberException { random = rng; singletons = new ArrayList<T>(pmf.size()); final double[] probs = new double[pmf.size()]; for (int i = 0; i < pmf.size(); i++) { final Pair<T, Double> 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); } /** * <p>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.</p> * * <p>Note that if {@code x1} and {@code x2} satisfy {@code x1.equals(x2)}, * or both are null, then {@code probability(x1) = probability(x2)}.</p> * * @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; } /** * <p>Return the probability mass function as a list of <value, probability> pairs.</p> * * <p>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).</p> * * @return the probability mass function. */ public List<Pair<T, Double>> getPmf() { final List<Pair<T, Double>> samples = new ArrayList<Pair<T, Double>>(probabilities.length); for (int i = 0; i < probabilities.length; i++) { samples.add(new Pair<T, Double>(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) { if (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. * <p> * 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; } }