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The Apache Commons RNG Sampling module provides samplers
for various distributions.
/*
* 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.rng.sampling.distribution;
import org.apache.commons.rng.UniformRandomProvider;
/**
* Compute a sample from {@code n} values each with an associated probability. If all unique items
* are assigned the same probability it is more efficient to use the {@link DiscreteUniformSampler}.
*
* The cumulative probability distribution is searched using a guide table to set an
* initial start point. This implementation is based on:
*
*
* Devroye, Luc (1986). Non-Uniform Random Variate Generation.
* New York: Springer-Verlag. Chapter 3.2.4 "The method of guide tables" p. 96.
*
*
* The size of the guide table can be controlled using a parameter. A larger guide table
* will improve performance at the cost of storage space.
*
* Sampling uses {@link UniformRandomProvider#nextDouble()}.
*
* @see
* Discrete probability distribution (Wikipedia)
* @since 1.3
*/
public final class GuideTableDiscreteSampler
implements SharedStateDiscreteSampler {
/** The default value for {@code alpha}. */
private static final double DEFAULT_ALPHA = 1.0;
/** Underlying source of randomness. */
private final UniformRandomProvider rng;
/**
* The cumulative probability table ({@code f(x)}).
*/
private final double[] cumulativeProbabilities;
/**
* The inverse cumulative probability guide table. This is a guide map between the cumulative
* probability (f(x)) and the value x. It is used to set the initial point for search
* of the cumulative probability table.
*
* The index in the map is obtained using {@code p * map.length} where {@code p} is the
* known cumulative probability {@code f(x)} or a uniform random deviate {@code u}. The value
* stored at the index is value {@code x+1} when {@code p = f(x)} such that it is the
* exclusive upper bound on the sample value {@code x} for searching the cumulative probability
* table {@code f(x)}. The search of the cumulative probability is towards zero.
*/
private final int[] guideTable;
/**
* @param rng Generator of uniformly distributed random numbers.
* @param cumulativeProbabilities The cumulative probability table ({@code f(x)}).
* @param guideTable The inverse cumulative probability guide table.
*/
private GuideTableDiscreteSampler(UniformRandomProvider rng,
double[] cumulativeProbabilities,
int[] guideTable) {
this.rng = rng;
this.cumulativeProbabilities = cumulativeProbabilities;
this.guideTable = guideTable;
}
/** {@inheritDoc} */
@Override
public int sample() {
// Compute a probability
final double u = rng.nextDouble();
// Initialise the search using the guide table to find an initial guess.
// The table provides an upper bound on the sample (x+1) for a known
// cumulative probability (f(x)).
int x = guideTable[getGuideTableIndex(u, guideTable.length)];
// Search down.
// In the edge case where u is 1.0 then 'x' will be 1 outside the range of the
// cumulative probability table and this will decrement to a valid range.
// In the case where 'u' is mapped to the same guide table index as a lower
// cumulative probability f(x) (due to rounding down) then this will not decrement
// and return the exclusive upper bound (x+1).
while (x != 0 && u <= cumulativeProbabilities[x - 1]) {
x--;
}
return x;
}
/** {@inheritDoc} */
@Override
public String toString() {
return "Guide table deviate [" + rng.toString() + "]";
}
/** {@inheritDoc} */
@Override
public SharedStateDiscreteSampler withUniformRandomProvider(UniformRandomProvider rng) {
return new GuideTableDiscreteSampler(rng, cumulativeProbabilities, guideTable);
}
/**
* Create a new sampler for an enumerated distribution using the given {@code probabilities}.
* The samples corresponding to each probability are assumed to be a natural sequence
* starting at zero.
*
* The size of the guide table is {@code probabilities.length}.
*
* @param rng Generator of uniformly distributed random numbers.
* @param probabilities The probabilities.
* @return the sampler
* @throws IllegalArgumentException if {@code probabilities} is null or empty, a
* probability is negative, infinite or {@code NaN}, or the sum of all
* probabilities is not strictly positive.
*/
public static SharedStateDiscreteSampler of(UniformRandomProvider rng,
double[] probabilities) {
return of(rng, probabilities, DEFAULT_ALPHA);
}
/**
* Create a new sampler for an enumerated distribution using the given {@code probabilities}.
* The samples corresponding to each probability are assumed to be a natural sequence
* starting at zero.
*
* The size of the guide table is {@code alpha * probabilities.length}.
*
* @param rng Generator of uniformly distributed random numbers.
* @param probabilities The probabilities.
* @param alpha The alpha factor used to set the guide table size.
* @return the sampler
* @throws IllegalArgumentException if {@code probabilities} is null or empty, a
* probability is negative, infinite or {@code NaN}, the sum of all
* probabilities is not strictly positive, or {@code alpha} is not strictly positive.
*/
public static SharedStateDiscreteSampler of(UniformRandomProvider rng,
double[] probabilities,
double alpha) {
validateParameters(probabilities, alpha);
final int size = probabilities.length;
final double[] cumulativeProbabilities = new double[size];
double sumProb = 0;
int count = 0;
for (final double prob : probabilities) {
InternalUtils.validateProbability(prob);
// Compute and store cumulative probability.
sumProb += prob;
cumulativeProbabilities[count++] = sumProb;
}
if (Double.isInfinite(sumProb) || sumProb <= 0) {
throw new IllegalArgumentException("Invalid sum of probabilities: " + sumProb);
}
// Note: The guide table is at least length 1. Compute the size avoiding overflow
// in case (alpha * size) is too large.
final int guideTableSize = (int) Math.ceil(alpha * size);
final int[] guideTable = new int[Math.max(guideTableSize, guideTableSize + 1)];
// Compute and store cumulative probability.
for (int x = 0; x < size; x++) {
final double norm = cumulativeProbabilities[x] / sumProb;
cumulativeProbabilities[x] = (norm < 1) ? norm : 1.0;
// Set the guide table value as an exclusive upper bound (x + 1)
final int index = getGuideTableIndex(cumulativeProbabilities[x], guideTable.length);
guideTable[index] = x + 1;
}
// Edge case for round-off
cumulativeProbabilities[size - 1] = 1.0;
// The final guide table entry is (maximum value of x + 1)
guideTable[guideTable.length - 1] = size;
// The first non-zero value in the guide table is from f(x=0).
// Any probabilities mapped below this must be sample x=0 so the
// table may initially be filled with zeros.
// Fill missing values in the guide table.
for (int i = 1; i < guideTable.length; i++) {
guideTable[i] = Math.max(guideTable[i - 1], guideTable[i]);
}
return new GuideTableDiscreteSampler(rng, cumulativeProbabilities, guideTable);
}
/**
* Validate the parameters.
*
* @param probabilities The probabilities.
* @param alpha The alpha factor used to set the guide table size.
* @throws IllegalArgumentException if {@code probabilities} is null or empty, or
* {@code alpha} is not strictly positive.
*/
private static void validateParameters(double[] probabilities, double alpha) {
if (probabilities == null || probabilities.length == 0) {
throw new IllegalArgumentException("Probabilities must not be empty.");
}
if (alpha <= 0) {
throw new IllegalArgumentException("Alpha must be strictly positive.");
}
}
/**
* Gets the guide table index for the probability. This is obtained using
* {@code p * (tableLength - 1)} so is inside the length of the table.
*
* @param p Cumulative probability.
* @param tableLength Table length.
* @return the guide table index.
*/
private static int getGuideTableIndex(double p, int tableLength) {
// Note: This is only ever called when p is in the range of the cumulative
// probability table. So assume 0 <= p <= 1.
return (int) (p * (tableLength - 1));
}
}