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 1455716 2013-03-12 21:12:21Z tn $
036 */
037 public abstract class AbstractIntegerDistribution implements IntegerDistribution, Serializable {
038
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 /**
068 * @param rng Random number generator.
069 * @since 3.1
070 */
071 protected AbstractIntegerDistribution(RandomGenerator rng) {
072 random = rng;
073 }
074
075 /**
076 * {@inheritDoc}
077 *
078 * The default implementation uses the identity
079 * <p>{@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}</p>
080 */
081 public double cumulativeProbability(int x0, int x1) throws NumberIsTooLargeException {
082 if (x1 < x0) {
083 throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
084 x0, x1, true);
085 }
086 return cumulativeProbability(x1) - cumulativeProbability(x0);
087 }
088
089 /**
090 * {@inheritDoc}
091 *
092 * The default implementation returns
093 * <ul>
094 * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li>
095 * <li>{@link #getSupportUpperBound()} for {@code p = 1}, and</li>
096 * <li>{@link #solveInverseCumulativeProbability(double, int, int)} for
097 * {@code 0 < p < 1}.</li>
098 * </ul>
099 */
100 public int inverseCumulativeProbability(final double p) throws OutOfRangeException {
101 if (p < 0.0 || p > 1.0) {
102 throw new OutOfRangeException(p, 0, 1);
103 }
104
105 int lower = getSupportLowerBound();
106 if (p == 0.0) {
107 return lower;
108 }
109 if (lower == Integer.MIN_VALUE) {
110 if (checkedCumulativeProbability(lower) >= p) {
111 return lower;
112 }
113 } else {
114 lower -= 1; // this ensures cumulativeProbability(lower) < p, which
115 // is important for the solving step
116 }
117
118 int upper = getSupportUpperBound();
119 if (p == 1.0) {
120 return upper;
121 }
122
123 // use the one-sided Chebyshev inequality to narrow the bracket
124 // cf. AbstractRealDistribution.inverseCumulativeProbability(double)
125 final double mu = getNumericalMean();
126 final double sigma = FastMath.sqrt(getNumericalVariance());
127 final boolean chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) ||
128 Double.isInfinite(sigma) || Double.isNaN(sigma) || sigma == 0.0);
129 if (chebyshevApplies) {
130 double k = FastMath.sqrt((1.0 - p) / p);
131 double tmp = mu - k * sigma;
132 if (tmp > lower) {
133 lower = ((int) Math.ceil(tmp)) - 1;
134 }
135 k = 1.0 / k;
136 tmp = mu + k * sigma;
137 if (tmp < upper) {
138 upper = ((int) Math.ceil(tmp)) - 1;
139 }
140 }
141
142 return solveInverseCumulativeProbability(p, lower, upper);
143 }
144
145 /**
146 * This is a utility function used by {@link
147 * #inverseCumulativeProbability(double)}. It assumes {@code 0 < p < 1} and
148 * that the inverse cumulative probability lies in the bracket {@code
149 * (lower, upper]}. The implementation does simple bisection to find the
150 * smallest {@code p}-quantile <code>inf{x in Z | P(X<=x) >= p}</code>.
151 *
152 * @param p the cumulative probability
153 * @param lower a value satisfying {@code cumulativeProbability(lower) < p}
154 * @param upper a value satisfying {@code p <= cumulativeProbability(upper)}
155 * @return the smallest {@code p}-quantile of this distribution
156 */
157 protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {
158 while (lower + 1 < upper) {
159 int xm = (lower + upper) / 2;
160 if (xm < lower || xm > upper) {
161 /*
162 * Overflow.
163 * There will never be an overflow in both calculation methods
164 * for xm at the same time
165 */
166 xm = lower + (upper - lower) / 2;
167 }
168
169 double pm = checkedCumulativeProbability(xm);
170 if (pm >= p) {
171 upper = xm;
172 } else {
173 lower = xm;
174 }
175 }
176 return upper;
177 }
178
179 /** {@inheritDoc} */
180 public void reseedRandomGenerator(long seed) {
181 random.setSeed(seed);
182 randomData.reSeed(seed);
183 }
184
185 /**
186 * {@inheritDoc}
187 *
188 * The default implementation uses the
189 * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling">
190 * inversion method</a>.
191 */
192 public int sample() {
193 return inverseCumulativeProbability(random.nextDouble());
194 }
195
196 /**
197 * {@inheritDoc}
198 *
199 * The default implementation generates the sample by calling
200 * {@link #sample()} in a loop.
201 */
202 public int[] sample(int sampleSize) {
203 if (sampleSize <= 0) {
204 throw new NotStrictlyPositiveException(
205 LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize);
206 }
207 int[] out = new int[sampleSize];
208 for (int i = 0; i < sampleSize; i++) {
209 out[i] = sample();
210 }
211 return out;
212 }
213
214 /**
215 * Computes the cumulative probability function and checks for {@code NaN}
216 * values returned. Throws {@code MathInternalError} if the value is
217 * {@code NaN}. Rethrows any exception encountered evaluating the cumulative
218 * probability function. Throws {@code MathInternalError} if the cumulative
219 * probability function returns {@code NaN}.
220 *
221 * @param argument input value
222 * @return the cumulative probability
223 * @throws MathInternalError if the cumulative probability is {@code NaN}
224 */
225 private double checkedCumulativeProbability(int argument)
226 throws MathInternalError {
227 double result = Double.NaN;
228 result = cumulativeProbability(argument);
229 if (Double.isNaN(result)) {
230 throw new MathInternalError(LocalizedFormats
231 .DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);
232 }
233 return result;
234 }
235 }