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 }