    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.math.distribution;
    018
    019    import java.io.Serializable;
    020
    021    import org.apache.commons.math.ConvergenceException;
    022    import org.apache.commons.math.MathException;
    023    import org.apache.commons.math.MathRuntimeException;
    024    import org.apache.commons.math.analysis.UnivariateRealFunction;
    025    import org.apache.commons.math.analysis.solvers.BrentSolver;
    026    import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils;
    027    import org.apache.commons.math.FunctionEvaluationException;
    028    import org.apache.commons.math.exception.util.LocalizedFormats;
    029    import org.apache.commons.math.random.RandomDataImpl;
    030    import org.apache.commons.math.util.FastMath;
    031
    032    /**
    033     * Base class for continuous distributions.  Default implementations are
    034     * provided for some of the methods that do not vary from distribution to
    035     * distribution.
    036     *
    037     * @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 f??vr. 2011) $
    038     */
    039    public abstract class AbstractContinuousDistribution
    040        extends AbstractDistribution
    041        implements ContinuousDistribution, Serializable {
    042
    043        /** Serializable version identifier */
    044        private static final long serialVersionUID = -38038050983108802L;
    045
    046        /**
    047         * RandomData instance used to generate samples from the distribution
    048         * @since 2.2
    049         */
    050        protected final RandomDataImpl randomData = new RandomDataImpl();
    051
    052        /**
    053         * Solver absolute accuracy for inverse cumulative computation
    054         * @since 2.1
    055         */
    056        private double solverAbsoluteAccuracy = BrentSolver.DEFAULT_ABSOLUTE_ACCURACY;
    057
    058        /**
    059         * Default constructor.
    060         */
    061        protected AbstractContinuousDistribution() {
    062            super();
    063        }
    064
    065        /**
    066         * Return the probability density for a particular point.
    067         * @param x  The point at which the density should be computed.
    068         * @return  The pdf at point x.
    069         * @throws MathRuntimeException if the specialized class hasn't implemented this function
    070         * @since 2.1
    071         */
    072        public double density(double x) throws MathRuntimeException {
    073            throw new MathRuntimeException(new UnsupportedOperationException(),
    074                    LocalizedFormats.NO_DENSITY_FOR_THIS_DISTRIBUTION);
    075        }
    076
    077        /**
    078         * For this distribution, X, this method returns the critical point x, such
    079         * that P(X &lt; x) = <code>p</code>.
    080         *
    081         * @param p the desired probability
    082         * @return x, such that P(X &lt; x) = <code>p</code>
    083         * @throws MathException if the inverse cumulative probability can not be
    084         *         computed due to convergence or other numerical errors.
    085         * @throws IllegalArgumentException if <code>p</code> is not a valid
    086         *         probability.
    087         */
    088        public double inverseCumulativeProbability(final double p)
    089            throws MathException {
    090            if (p < 0.0 || p > 1.0) {
    091                throw MathRuntimeException.createIllegalArgumentException(
    092                      LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
    093            }
    094
    095            // by default, do simple root finding using bracketing and default solver.
    096            // subclasses can override if there is a better method.
    097            UnivariateRealFunction rootFindingFunction =
    098                new UnivariateRealFunction() {
    099                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    }