/*
* 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.math4.distribution;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MathArithmeticException;
import org.apache.commons.math4.exception.NotANumberException;
import org.apache.commons.math4.exception.NotFiniteNumberException;
import org.apache.commons.math4.exception.NotPositiveException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.math4.util.Pair;
/**
* <p>Implementation of a real-valued {@link EnumeratedDistribution}.
*
* <p>Values with zero-probability are allowed but they do not extend the
* support.<br>
* Duplicate values are allowed. Probabilities of duplicate values are combined
* when computing cumulative probabilities and statistics.</p>
*
* @since 3.2
*/
public class EnumeratedRealDistribution extends AbstractRealDistribution {
/** Serializable UID. */
private static final long serialVersionUID = 20160311L;
/**
* {@link EnumeratedDistribution} (using the {@link Double} wrapper)
* used to generate the pmf.
*/
protected final EnumeratedDistribution<Double> innerDistribution;
/**
* Create a discrete real-valued distribution using the given random number generator
* and probability mass function enumeration.
*
* @param singletons array of random variable values.
* @param probabilities array of probabilities.
* @throws DimensionMismatchException if
* {@code singletons.length != probabilities.length}
* @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 EnumeratedRealDistribution(final double[] singletons,
final double[] probabilities)
throws DimensionMismatchException,
NotPositiveException,
MathArithmeticException,
NotFiniteNumberException,
NotANumberException {
innerDistribution = new EnumeratedDistribution<>(createDistribution(singletons, probabilities));
}
/**
* Creates a discrete real-valued distribution from the input data.
* Values are assigned mass based on their frequency.
*
* @param data input dataset
*/
public EnumeratedRealDistribution(final double[] data) {
final Map<Double, Integer> dataMap = new HashMap<>();
for (double value : data) {
Integer count = dataMap.get(value);
if (count == null) {
count = 0;
}
dataMap.put(value, ++count);
}
final int massPoints = dataMap.size();
final double denom = data.length;
final double[] values = new double[massPoints];
final double[] probabilities = new double[massPoints];
int index = 0;
for (Entry<Double, Integer> entry : dataMap.entrySet()) {
values[index] = entry.getKey();
probabilities[index] = entry.getValue().intValue() / denom;
index++;
}
innerDistribution = new EnumeratedDistribution<>(createDistribution(values, probabilities));
}
/**
* Create the list of Pairs representing the distribution from singletons and probabilities.
*
* @param singletons values
* @param probabilities probabilities
* @return list of value/probability pairs
*/
private static List<Pair<Double, Double>> createDistribution(double[] singletons, double[] probabilities) {
if (singletons.length != probabilities.length) {
throw new DimensionMismatchException(probabilities.length, singletons.length);
}
final List<Pair<Double, Double>> samples = new ArrayList<>(singletons.length);
for (int i = 0; i < singletons.length; i++) {
samples.add(new Pair<>(singletons[i], probabilities[i]));
}
return samples;
}
/**
* {@inheritDoc}
*/
@Override
public double probability(final double x) {
return innerDistribution.probability(x);
}
/**
* 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.
*
* @param x the point at which the PMF is evaluated
* @return the value of the probability mass function at point {@code x}
*/
@Override
public double density(final double x) {
return probability(x);
}
/**
* {@inheritDoc}
*/
@Override
public double cumulativeProbability(final double x) {
double probability = 0;
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
if (sample.getKey() <= x) {
probability += sample.getValue();
}
}
return probability;
}
/**
* {@inheritDoc}
*/
@Override
public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
double probability = 0;
double x = getSupportLowerBound();
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
if (sample.getValue() == 0.0) {
continue;
}
probability += sample.getValue();
x = sample.getKey();
if (probability >= p) {
break;
}
}
return x;
}
/**
* {@inheritDoc}
*
* @return {@code sum(singletons[i] * probabilities[i])}
*/
@Override
public double getNumericalMean() {
double mean = 0;
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
mean += sample.getValue() * sample.getKey();
}
return mean;
}
/**
* {@inheritDoc}
*
* @return {@code sum((singletons[i] - mean) ^ 2 * probabilities[i])}
*/
@Override
public double getNumericalVariance() {
double mean = 0;
double meanOfSquares = 0;
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
mean += sample.getValue() * sample.getKey();
meanOfSquares += sample.getValue() * sample.getKey() * sample.getKey();
}
return meanOfSquares - mean * mean;
}
/**
* {@inheritDoc}
*
* Returns the lowest value with non-zero probability.
*
* @return the lowest value with non-zero probability.
*/
@Override
public double getSupportLowerBound() {
double min = Double.POSITIVE_INFINITY;
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
if (sample.getKey() < min && sample.getValue() > 0) {
min = sample.getKey();
}
}
return min;
}
/**
* {@inheritDoc}
*
* Returns the highest value with non-zero probability.
*
* @return the highest value with non-zero probability.
*/
@Override
public double getSupportUpperBound() {
double max = Double.NEGATIVE_INFINITY;
for (final Pair<Double, Double> sample : innerDistribution.getPmf()) {
if (sample.getKey() > max && sample.getValue() > 0) {
max = sample.getKey();
}
}
return max;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
@Override
public boolean isSupportConnected() {
return true;
}
/** {@inheritDoc} */
@Override
public RealDistribution.Sampler createSampler(final UniformRandomProvider rng) {
return new RealDistribution.Sampler() {
/** Delegate. */
private final EnumeratedDistribution<Double>.Sampler inner =
innerDistribution.createSampler(rng);
/** {@inheritDoc} */
@Override
public double sample() {
return inner.sample();
}
};
}
}