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     */
017    package org.apache.commons.math3.distribution;
018    
019    import java.io.Serializable;
020    
021    import org.apache.commons.math3.exception.MathInternalError;
022    import org.apache.commons.math3.exception.NotStrictlyPositiveException;
023    import org.apache.commons.math3.exception.NumberIsTooLargeException;
024    import org.apache.commons.math3.exception.OutOfRangeException;
025    import org.apache.commons.math3.exception.util.LocalizedFormats;
026    import org.apache.commons.math3.random.RandomGenerator;
027    import org.apache.commons.math3.random.RandomDataImpl;
028    import org.apache.commons.math3.util.FastMath;
029    
030    /**
031     * Base class for integer-valued discrete distributions.  Default
032     * implementations are provided for some of the methods that do not vary
033     * from distribution to distribution.
034     *
035     * @version $Id: AbstractIntegerDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $
036     */
037    public abstract class AbstractIntegerDistribution
038    implements IntegerDistribution, Serializable {
039        /** Serializable version identifier */
040        private static final long serialVersionUID = -1146319659338487221L;
041    
042         /**
043          * RandomData instance used to generate samples from the distribution.
044          * @deprecated As of 3.1, to be removed in 4.0. Please use the
045          * {@link #random} instance variable instead.
046          */
047        @Deprecated
048        protected final RandomDataImpl randomData = new RandomDataImpl();
049    
050        /**
051         * RNG instance used to generate samples from the distribution.
052         * @since 3.1
053         */
054        protected final RandomGenerator random;
055    
056        /**
057         * @deprecated As of 3.1, to be removed in 4.0. Please use
058         * {@link #AbstractIntegerDistribution(RandomGenerator)} instead.
059         */
060        @Deprecated
061        protected AbstractIntegerDistribution() {
062            // Legacy users are only allowed to access the deprecated "randomData".
063            // New users are forbidden to use this constructor.
064            random = null;
065        }
066        /**
067         * @param rng Random number generator.
068         * @since 3.1
069         */
070        protected AbstractIntegerDistribution(RandomGenerator rng) {
071            random = rng;
072        }
073    
074        /**
075         * {@inheritDoc}
076         *
077         * The default implementation uses the identity
078         * <p>{@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}</p>
079         */
080        public double cumulativeProbability(int x0, int x1) throws NumberIsTooLargeException {
081            if (x1 < x0) {
082                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
083                        x0, x1, true);
084            }
085            return cumulativeProbability(x1) - cumulativeProbability(x0);
086        }
087    
088        /**
089         * {@inheritDoc}
090         *
091         * The default implementation returns
092         * <ul>
093         * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li>
094         * <li>{@link #getSupportUpperBound()} for {@code p = 1}, and</li>
095         * <li>{@link #solveInverseCumulativeProbability(double, int, int)} for
096         *     {@code 0 < p < 1}.</li>
097         * </ul>
098         */
099        public int inverseCumulativeProbability(final double p) throws OutOfRangeException {
100            if (p < 0.0 || p > 1.0) {
101                throw new OutOfRangeException(p, 0, 1);
102            }
103    
104            int lower = getSupportLowerBound();
105            if (p == 0.0) {
106                return lower;
107            }
108            if (lower == Integer.MIN_VALUE) {
109                if (checkedCumulativeProbability(lower) >= p) {
110                    return lower;
111                }
112            } else {
113                lower -= 1; // this ensures cumulativeProbability(lower) < p, which
114                            // is important for the solving step
115            }
116    
117            int upper = getSupportUpperBound();
118            if (p == 1.0) {
119                return upper;
120            }
121    
122            // use the one-sided Chebyshev inequality to narrow the bracket
123            // cf. AbstractRealDistribution.inverseCumulativeProbability(double)
124            final double mu = getNumericalMean();
125            final double sigma = FastMath.sqrt(getNumericalVariance());
126            final boolean chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) ||
127                    Double.isInfinite(sigma) || Double.isNaN(sigma) || sigma == 0.0);
128            if (chebyshevApplies) {
129                double k = FastMath.sqrt((1.0 - p) / p);
130                double tmp = mu - k * sigma;
131                if (tmp > lower) {
132                    lower = ((int) Math.ceil(tmp)) - 1;
133                }
134                k = 1.0 / k;
135                tmp = mu + k * sigma;
136                if (tmp < upper) {
137                    upper = ((int) Math.ceil(tmp)) - 1;
138                }
139            }
140    
141            return solveInverseCumulativeProbability(p, lower, upper);
142        }
143    
144        /**
145         * This is a utility function used by {@link
146         * #inverseCumulativeProbability(double)}. It assumes {@code 0 < p < 1} and
147         * that the inverse cumulative probability lies in the bracket {@code
148         * (lower, upper]}. The implementation does simple bisection to find the
149         * smallest {@code p}-quantile <code>inf{x in Z | P(X<=x) >= p}</code>.
150         *
151         * @param p the cumulative probability
152         * @param lower a value satisfying {@code cumulativeProbability(lower) < p}
153         * @param upper a value satisfying {@code p <= cumulativeProbability(upper)}
154         * @return the smallest {@code p}-quantile of this distribution
155         */
156        protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {
157            while (lower + 1 < upper) {
158                int xm = (lower + upper) / 2;
159                if (xm < lower || xm > upper) {
160                    /*
161                     * Overflow.
162                     * There will never be an overflow in both calculation methods
163                     * for xm at the same time
164                     */
165                    xm = lower + (upper - lower) / 2;
166                }
167    
168                double pm = checkedCumulativeProbability(xm);
169                if (pm >= p) {
170                    upper = xm;
171                } else {
172                    lower = xm;
173                }
174            }
175            return upper;
176        }
177    
178        /** {@inheritDoc} */
179        public void reseedRandomGenerator(long seed) {
180            random.setSeed(seed);
181            randomData.reSeed(seed);
182        }
183    
184        /**
185         * {@inheritDoc}
186         *
187         * The default implementation uses the
188         * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling">
189         * inversion method</a>.
190         */
191        public int sample() {
192            return inverseCumulativeProbability(random.nextDouble());
193        }
194    
195        /**
196         * {@inheritDoc}
197         *
198         * The default implementation generates the sample by calling
199         * {@link #sample()} in a loop.
200         */
201        public int[] sample(int sampleSize) {
202            if (sampleSize <= 0) {
203                throw new NotStrictlyPositiveException(
204                        LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize);
205            }
206            int[] out = new int[sampleSize];
207            for (int i = 0; i < sampleSize; i++) {
208                out[i] = sample();
209            }
210            return out;
211        }
212    
213        /**
214         * Computes the cumulative probability function and checks for {@code NaN}
215         * values returned. Throws {@code MathInternalError} if the value is
216         * {@code NaN}. Rethrows any exception encountered evaluating the cumulative
217         * probability function. Throws {@code MathInternalError} if the cumulative
218         * probability function returns {@code NaN}.
219         *
220         * @param argument input value
221         * @return the cumulative probability
222         * @throws MathInternalError if the cumulative probability is {@code NaN}
223         */
224        private double checkedCumulativeProbability(int argument)
225            throws MathInternalError {
226            double result = Double.NaN;
227            result = cumulativeProbability(argument);
228            if (Double.isNaN(result)) {
229                throw new MathInternalError(LocalizedFormats
230                        .DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);
231            }
232            return result;
233        }
234    }