1/*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements.  See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License.  You may obtain a copy of the License at
8 *
9 *      http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17package org.apache.commons.math.distribution;
18
19import java.io.Serializable;
20
21import org.apache.commons.math.ConvergenceException;
22import org.apache.commons.math.MathException;
23import org.apache.commons.math.MathRuntimeException;
24import org.apache.commons.math.analysis.UnivariateRealFunction;
25import org.apache.commons.math.analysis.solvers.BrentSolver;
26import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils;
27import org.apache.commons.math.FunctionEvaluationException;
28import org.apache.commons.math.exception.util.LocalizedFormats;
29import org.apache.commons.math.random.RandomDataImpl;
30import org.apache.commons.math.util.FastMath;
31
32/**
33 * Base class for continuous distributions.  Default implementations are
34 * provided for some of the methods that do not vary from distribution to
35 * distribution.
36 *
37 * @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $
38 */
39public abstract class AbstractContinuousDistribution
40    extends AbstractDistribution
41    implements ContinuousDistribution, Serializable {
42
43    /** Serializable version identifier */
44    private static final long serialVersionUID = -38038050983108802L;
45
46    /**
47     * RandomData instance used to generate samples from the distribution
48     * @since 2.2
49     */
50    protected final RandomDataImpl randomData = new RandomDataImpl();
51
52    /**
53     * Solver absolute accuracy for inverse cumulative computation
54     * @since 2.1
55     */
56    private double solverAbsoluteAccuracy = BrentSolver.DEFAULT_ABSOLUTE_ACCURACY;
57
58    /**
59     * Default constructor.
60     */
61    protected AbstractContinuousDistribution() {
62        super();
63    }
64
65    /**
66     * Return the probability density for a particular point.
67     * @param x  The point at which the density should be computed.
68     * @return  The pdf at point x.
69     * @throws MathRuntimeException if the specialized class hasn't implemented this function
70     * @since 2.1
71     */
72    public double density(double x) throws MathRuntimeException {
73        throw new MathRuntimeException(new UnsupportedOperationException(),
74                LocalizedFormats.NO_DENSITY_FOR_THIS_DISTRIBUTION);
75    }
76
77    /**
78     * For this distribution, X, this method returns the critical point x, such
79     * that P(X &lt; x) = <code>p</code>.
80     *
81     * @param p the desired probability
82     * @return x, such that P(X &lt; x) = <code>p</code>
83     * @throws MathException if the inverse cumulative probability can not be
84     *         computed due to convergence or other numerical errors.
85     * @throws IllegalArgumentException if <code>p</code> is not a valid
86     *         probability.
87     */
88    public double inverseCumulativeProbability(final double p)
89        throws MathException {
90        if (p < 0.0 || p > 1.0) {
91            throw MathRuntimeException.createIllegalArgumentException(
92                  LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
93        }
94
95        // by default, do simple root finding using bracketing and default solver.
96        // subclasses can override if there is a better method.
97        UnivariateRealFunction rootFindingFunction =
98            new UnivariateRealFunction() {
99            public double value(double x) throws FunctionEvaluationException {
100                double ret = Double.NaN;
101                try {
102                    ret = cumulativeProbability(x) - p;
103                } catch (MathException ex) {
104                    throw new FunctionEvaluationException(x, ex.getSpecificPattern(), ex.getGeneralPattern(), ex.getArguments());
105                }
106                if (Double.isNaN(ret)) {
107                    throw new FunctionEvaluationException(x, LocalizedFormats.CUMULATIVE_PROBABILITY_RETURNED_NAN, x, p);
108                }
109                return ret;
110            }
111        };
112
113        // Try to bracket root, test domain endpoints if this fails
114        double lowerBound = getDomainLowerBound(p);
115        double upperBound = getDomainUpperBound(p);
116        double[] bracket = null;
117        try {
118            bracket = UnivariateRealSolverUtils.bracket(
119                    rootFindingFunction, getInitialDomain(p),
120                    lowerBound, upperBound);
121        }  catch (ConvergenceException ex) {
122            /*
123             * Check domain endpoints to see if one gives value that is within
124             * the default solver's defaultAbsoluteAccuracy of 0 (will be the
125             * case if density has bounded support and p is 0 or 1).
126             */
127            if (FastMath.abs(rootFindingFunction.value(lowerBound)) < getSolverAbsoluteAccuracy()) {
128                return lowerBound;
129            }
130            if (FastMath.abs(rootFindingFunction.value(upperBound)) < getSolverAbsoluteAccuracy()) {
131                return upperBound;
132            }
133            // Failed bracket convergence was not because of corner solution
134            throw new MathException(ex);
135        }
136
137        // find root
138        double root = UnivariateRealSolverUtils.solve(rootFindingFunction,
139                // override getSolverAbsoluteAccuracy() to use a Brent solver with
140                // absolute accuracy different from BrentSolver default
141                bracket[0],bracket[1], getSolverAbsoluteAccuracy());
142        return root;
143    }
144
145    /**
146     * Reseeds the random generator used to generate samples.
147     *
148     * @param seed the new seed
149     * @since 2.2
150     */
151    public void reseedRandomGenerator(long seed) {
152        randomData.reSeed(seed);
153    }
154
155    /**
156     * Generates a random value sampled from this distribution. The default
157     * implementation uses the
158     * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> inversion method.</a>
159     *
160     * @return random value
161     * @since 2.2
162     * @throws MathException if an error occurs generating the random value
163     */
164    public double sample() throws MathException {
165        return randomData.nextInversionDeviate(this);
166    }
167
168    /**
169     * Generates a random sample from the distribution.  The default implementation
170     * generates the sample by calling {@link #sample()} in a loop.
171     *
172     * @param sampleSize number of random values to generate
173     * @since 2.2
174     * @return an array representing the random sample
175     * @throws MathException if an error occurs generating the sample
176     * @throws IllegalArgumentException if sampleSize is not positive
177     */
178    public double[] sample(int sampleSize) throws MathException {
179        if (sampleSize <= 0) {
180            MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, sampleSize);
181        }
182        double[] out = new double[sampleSize];
183        for (int i = 0; i < sampleSize; i++) {
184            out[i] = sample();
185        }
186        return out;
187    }
188
189    /**
190     * Access the initial domain value, based on <code>p</code>, used to
191     * bracket a CDF root.  This method is used by
192     * {@link #inverseCumulativeProbability(double)} to find critical values.
193     *
194     * @param p the desired probability for the critical value
195     * @return initial domain value
196     */
197    protected abstract double getInitialDomain(double p);
198
199    /**
200     * Access the domain value lower bound, based on <code>p</code>, used to
201     * bracket a CDF root.  This method is used by
202     * {@link #inverseCumulativeProbability(double)} to find critical values.
203     *
204     * @param p the desired probability for the critical value
205     * @return domain value lower bound, i.e.
206     *         P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
207     */
208    protected abstract double getDomainLowerBound(double p);
209
210    /**
211     * Access the domain value upper bound, based on <code>p</code>, used to
212     * bracket a CDF root.  This method is used by
213     * {@link #inverseCumulativeProbability(double)} to find critical values.
214     *
215     * @param p the desired probability for the critical value
216     * @return domain value upper bound, i.e.
217     *         P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
218     */
219    protected abstract double getDomainUpperBound(double p);
220
221    /**
222     * Returns the solver absolute accuracy for inverse cumulative computation.
223     *
224     * @return the maximum absolute error in inverse cumulative probability estimates
225     * @since 2.1
226     */
227    protected double getSolverAbsoluteAccuracy() {
228        return solverAbsoluteAccuracy;
229    }
230
231}
232