/*
* 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.
*
* @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;
}
}