EnumeratedDistribution.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.apache.commons.math4.legacy.distribution;

  19. import java.lang.reflect.Array;
  20. import java.util.ArrayList;
  21. import java.util.List;

  23. import org.apache.commons.math4.legacy.exception.MathArithmeticException;
  24. import org.apache.commons.math4.legacy.exception.NotANumberException;
  25. import org.apache.commons.math4.legacy.exception.NotFiniteNumberException;
  26. import org.apache.commons.math4.legacy.exception.NotPositiveException;
  27. import org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException;
  28. import org.apache.commons.math4.legacy.exception.NullArgumentException;
  29. import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
  30. import org.apache.commons.rng.UniformRandomProvider;
  31. import org.apache.commons.rng.sampling.DiscreteProbabilityCollectionSampler;
  32. import org.apache.commons.math4.legacy.core.MathArrays;
  33. import org.apache.commons.math4.legacy.core.Pair;

  35. /**
  36.  * <p>A generic implementation of a
  37.  * <a href="http://en.wikipedia.org/wiki/Probability_distribution#Discrete_probability_distribution">
  38.  * discrete probability distribution (Wikipedia)</a> over a finite sample space,
  39.  * based on an enumerated list of &lt;value, probability&gt; pairs.  Input probabilities must all be non-negative,
  40.  * but zero values are allowed and their sum does not have to equal one. Constructors will normalize input
  41.  * probabilities to make them sum to one.</p>
  42.  *
  43.  * <p>The list of &lt;value, probability&gt; pairs does not, strictly speaking, have to be a function and it can
  44.  * contain null values.  The pmf created by the constructor will combine probabilities of equal values and
  45.  * will treat null values as equal.  For example, if the list of pairs &lt;"dog", 0.2&gt;, &lt;null, 0.1&gt;,
  46.  * &lt;"pig", 0.2&gt;, &lt;"dog", 0.1&gt;, &lt;null, 0.4&gt; is provided to the constructor, the resulting
  47.  * pmf will assign mass of 0.5 to null, 0.3 to "dog" and 0.2 to pig.</p>
  48.  *
  49.  * @param <T> type of the elements in the sample space.
  50.  * @since 3.2
  51.  */
  52. public class EnumeratedDistribution<T> {
  53.     /**
  54.      * List of random variable values.
  55.      */
  56.     private final List<T> singletons;
  57.     /**
  58.      * Probabilities of respective random variable values. For i = 0, ..., singletons.size() - 1,
  59.      * probability[i] is the probability that a random variable following this distribution takes
  60.      * the value singletons[i].
  61.      */
  62.     private final double[] probabilities;
  63.     /**
  64.      * Cumulative probabilities, cached to speed up sampling.
  65.      */
  66.     private final double[] cumulativeProbabilities;

  68.     /**
  69.      * Create an enumerated distribution using the given random number generator
  70.      * and probability mass function enumeration.
  71.      *
  72.      * @param pmf probability mass function enumerated as a list of
  73.      * {@code <T, probability>} pairs.
  74.      * @throws NotPositiveException if any of the probabilities are negative.
  75.      * @throws NotFiniteNumberException if any of the probabilities are infinite.
  76.      * @throws NotANumberException if any of the probabilities are NaN.
  77.      * @throws MathArithmeticException all of the probabilities are 0.
  78.      */
  79.     public EnumeratedDistribution(final List<Pair<T, Double>> pmf)
  80.         throws NotPositiveException,
  81.                MathArithmeticException,
  82.                NotFiniteNumberException,
  83.                NotANumberException {
  84.         singletons = new ArrayList<>(pmf.size());
  85.         final double[] probs = new double[pmf.size()];
  86.         int count = 0;
  87.         for (Pair<T, Double> sample : pmf) {
  88.             singletons.add(sample.getKey());
  89.             final double p = sample.getValue();
  90.             if (p < 0) {
  91.                 throw new NotPositiveException(sample.getValue());
  92.             }
  93.             if (Double.isInfinite(p)) {
  94.                 throw new NotFiniteNumberException(p);
  95.             }
  96.             if (Double.isNaN(p)) {
  97.                 throw new NotANumberException();
  98.             }
  99.             probs[count++] = p;
  100.         }

  102.         probabilities = MathArrays.normalizeArray(probs, 1.0);

  104.         cumulativeProbabilities = new double[probabilities.length];
  105.         double sum = 0;
  106.         for (int i = 0; i < probabilities.length; i++) {
  107.             sum += probabilities[i];
  108.             cumulativeProbabilities[i] = sum;
  109.         }
  110.     }

  112.     /**
  113.      * <p>For a random variable {@code X} whose values are distributed according to
  114.      * this distribution, this method returns {@code P(X = x)}. In other words,
  115.      * this method represents the probability mass function (PMF) for the
  116.      * distribution.</p>
  117.      *
  118.      * <p>Note that if {@code x1} and {@code x2} satisfy {@code x1.equals(x2)},
  119.      * or both are null, then {@code probability(x1) = probability(x2)}.</p>
  120.      *
  121.      * @param x the point at which the PMF is evaluated
  122.      * @return the value of the probability mass function at {@code x}
  123.      */
  124.     double probability(final T x) {
  125.         double probability = 0;

  127.         for (int i = 0; i < probabilities.length; i++) {
  128.             if ((x == null && singletons.get(i) == null) ||
  129.                 (x != null && x.equals(singletons.get(i)))) {
  130.                 probability += probabilities[i];
  131.             }
  132.         }

  134.         return probability;
  135.     }

  137.     /**
  138.      * <p>Return the probability mass function as a list of &lt;value, probability&gt; pairs.</p>
  139.      *
  140.      * <p>Note that if duplicate and / or null values were provided to the constructor
  141.      * when creating this EnumeratedDistribution, the returned list will contain these
  142.      * values.  If duplicates values exist, what is returned will not represent
  143.      * a pmf (i.e., it is up to the caller to consolidate duplicate mass points).</p>
  144.      *
  145.      * @return the probability mass function.
  146.      */
  147.     public List<Pair<T, Double>> getPmf() {
  148.         final List<Pair<T, Double>> samples = new ArrayList<>(probabilities.length);

  150.         for (int i = 0; i < probabilities.length; i++) {
  151.             samples.add(new Pair<>(singletons.get(i), probabilities[i]));
  152.         }

  154.         return samples;
  155.     }

  157.     /**
  158.      * Creates a {@link Sampler}.
  159.      *
  160.      * @param rng Random number generator.
  161.      * @return a new sampler instance.
  162.      */
  163.     public Sampler createSampler(final UniformRandomProvider rng) {
  164.         return new Sampler(rng);
  165.     }

  167.     /**
  168.      * Sampler functionality.
  169.      *
  170.      * <ul>
  171.      *  <li>
  172.      *   The cumulative probability distribution is created (and sampled from)
  173.      *   using the input order of the {@link EnumeratedDistribution#EnumeratedDistribution(List)
  174.      *   constructor arguments}: A different input order will create a different
  175.      *   sequence of samples.
  176.      *   The samples will only be reproducible with the same RNG starting from
  177.      *   the same RNG state and the same input order to constructor.
  178.      *  </li>
  179.      *  <li>
  180.      *   The minimum supported probability is 2<sup>-53</sup>.
  181.      *  </li>
  182.      * </ul>
  183.      */
  184.     public class Sampler {
  185.         /** Underlying sampler. */
  186.         private final DiscreteProbabilityCollectionSampler<T> sampler;

  188.         /**
  189.          * @param rng Random number generator.
  190.          */
  191.         Sampler(UniformRandomProvider rng) {
  192.             sampler = new DiscreteProbabilityCollectionSampler<>(rng, singletons, probabilities);
  193.         }

  195.         /**
  196.          * Generates a random value sampled from this distribution.
  197.          *
  198.          * @return a random value.
  199.          */
  200.         public T sample() {
  201.             return sampler.sample();
  202.         }

  204.         /**
  205.          * Generates a random sample from the distribution.
  206.          *
  207.          * @param sampleSize the number of random values to generate.
  208.          * @return an array representing the random sample.
  209.          * @throws NotStrictlyPositiveException if {@code sampleSize} is not
  210.          * positive.
  211.          */
  212.         public Object[] sample(int sampleSize) throws NotStrictlyPositiveException {
  213.             if (sampleSize <= 0) {
  214.                 throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES,
  215.                                                        sampleSize);
  216.             }

  218.             final Object[] out = new Object[sampleSize];

  220.             for (int i = 0; i < sampleSize; i++) {
  221.                 out[i] = sample();
  222.             }

  224.             return out;
  225.         }

  227.         /**
  228.          * Generates a random sample from the distribution.
  229.          * <p>
  230.          * If the requested samples fit in the specified array, it is returned
  231.          * therein. Otherwise, a new array is allocated with the runtime type of
  232.          * the specified array and the size of this collection.
  233.          *
  234.          * @param sampleSize the number of random values to generate.
  235.          * @param array the array to populate.
  236.          * @return an array representing the random sample.
  237.          * @throws NotStrictlyPositiveException if {@code sampleSize} is not positive.
  238.          * @throws NullArgumentException if {@code array} is null
  239.          */
  240.         public T[] sample(int sampleSize, final T[] array) throws NotStrictlyPositiveException {
  241.             if (sampleSize <= 0) {
  242.                 throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize);
  243.             }

  245.             if (array == null) {
  246.                 throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
  247.             }

  249.             T[] out;
  250.             if (array.length < sampleSize) {
  251.                 @SuppressWarnings("unchecked") // safe as both are of type T
  252.                 final T[] unchecked = (T[]) Array.newInstance(array.getClass().getComponentType(), sampleSize);
  253.                 out = unchecked;
  254.             } else {
  255.                 out = array;
  256.             }

  258.             for (int i = 0; i < sampleSize; i++) {
  259.                 out[i] = sample();
  260.             }

  262.             return out;
  263.         }
  264.     }
  265. }
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