001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.rng.sampling.distribution;
018
019import org.apache.commons.rng.UniformRandomProvider;
020
021/**
022 * Sampling from an <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">exponential distribution</a>.
023 *
024 * <p>Sampling uses:</p>
025 *
026 * <ul>
027 *   <li>{@link UniformRandomProvider#nextLong()}
028 *   <li>{@link UniformRandomProvider#nextDouble()}
029 * </ul>
030 *
031 * @since 1.0
032 */
033public class AhrensDieterExponentialSampler
034    extends SamplerBase
035    implements SharedStateContinuousSampler {
036    /**
037     * Table containing the constants
038     * \( q_i = sum_{j=1}^i (\ln 2)^j / j! = \ln 2 + (\ln 2)^2 / 2 + ... + (\ln 2)^i / i! \)
039     * until the largest representable fraction below 1 is exceeded.
040     *
041     * Note that
042     * \( 1 = 2 - 1 = \exp(\ln 2) - 1 = sum_{n=1}^\infinity (\ln 2)^n / n! \)
043     * thus \( q_i \rightarrow 1 as i \rightarrow +\infinity \),
044     * so the higher \( i \), the closer we get to 1 (the series is not alternating).
045     *
046     * By trying, n = 16 in Java is enough to reach 1.
047     */
048    private static final double[] EXPONENTIAL_SA_QI = new double[16];
049    /** The mean of this distribution. */
050    private final double mean;
051    /** Underlying source of randomness. */
052    private final UniformRandomProvider rng;
053
054    //
055    // Initialize tables.
056    //
057    static {
058        //
059        // Filling EXPONENTIAL_SA_QI table.
060        // Note that we don't want qi = 0 in the table.
061        //
062        final double ln2 = Math.log(2);
063        double qi = 0;
064
065        for (int i = 0; i < EXPONENTIAL_SA_QI.length; i++) {
066            qi += Math.pow(ln2, i + 1.0) / InternalUtils.factorial(i + 1);
067            EXPONENTIAL_SA_QI[i] = qi;
068        }
069    }
070
071    /**
072     * @param rng Generator of uniformly distributed random numbers.
073     * @param mean Mean of this distribution.
074     * @throws IllegalArgumentException if {@code mean <= 0}
075     */
076    public AhrensDieterExponentialSampler(UniformRandomProvider rng,
077                                          double mean) {
078        super(null);
079        if (mean <= 0) {
080            throw new IllegalArgumentException("mean is not strictly positive: " + mean);
081        }
082        this.rng = rng;
083        this.mean = mean;
084    }
085
086    /**
087     * @param rng Generator of uniformly distributed random numbers.
088     * @param source Source to copy.
089     */
090    private AhrensDieterExponentialSampler(UniformRandomProvider rng,
091                                           AhrensDieterExponentialSampler source) {
092        super(null);
093        this.rng = rng;
094        this.mean = source.mean;
095    }
096
097    /** {@inheritDoc} */
098    @Override
099    public double sample() {
100        // Step 1:
101        double a = 0;
102        // Avoid u=0 which creates an infinite loop
103        double u = InternalUtils.makeNonZeroDouble(rng.nextLong());
104
105        // Step 2 and 3:
106        while (u < 0.5) {
107            a += EXPONENTIAL_SA_QI[0];
108            u *= 2;
109        }
110
111        // Step 4 (now u >= 0.5):
112        u += u - 1;
113
114        // Step 5:
115        if (u <= EXPONENTIAL_SA_QI[0]) {
116            return mean * (a + u);
117        }
118
119        // Step 6:
120        int i = 0; // Should be 1, be we iterate before it in while using 0.
121        double u2 = rng.nextDouble();
122        double umin = u2;
123
124        // Step 7 and 8:
125        do {
126            ++i;
127            u2 = rng.nextDouble();
128
129            if (u2 < umin) {
130                umin = u2;
131            }
132
133            // Step 8:
134        } while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1.
135
136        return mean * (a + umin * EXPONENTIAL_SA_QI[0]);
137    }
138
139    /** {@inheritDoc} */
140    @Override
141    public String toString() {
142        return "Ahrens-Dieter Exponential deviate [" + rng.toString() + "]";
143    }
144
145    /**
146     * {@inheritDoc}
147     *
148     * @since 1.3
149     */
150    @Override
151    public SharedStateContinuousSampler withUniformRandomProvider(UniformRandomProvider rng) {
152        return new AhrensDieterExponentialSampler(rng, this);
153    }
154
155    /**
156     * Create a new exponential distribution sampler.
157     *
158     * @param rng Generator of uniformly distributed random numbers.
159     * @param mean Mean of the distribution.
160     * @return the sampler
161     * @throws IllegalArgumentException if {@code mean <= 0}
162     * @since 1.3
163     */
164    public static SharedStateContinuousSampler of(UniformRandomProvider rng,
165                                                  double mean) {
166        return new AhrensDieterExponentialSampler(rng, mean);
167    }
168}