/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.solvers.BrentSolver;
import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.random.RandomDataImpl;
import org.apache.commons.math.util.FastMath;
/**
* Base class for continuous distributions. Default implementations are
* provided for some of the methods that do not vary from distribution to
* distribution.
*
* @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $
*/
public abstract class AbstractContinuousDistribution
extends AbstractDistribution
implements ContinuousDistribution, Serializable {
/** Serializable version identifier */
private static final long serialVersionUID = -38038050983108802L;
/**
* RandomData instance used to generate samples from the distribution
* @since 2.2
*/
protected final RandomDataImpl randomData = new RandomDataImpl();
/**
* Solver absolute accuracy for inverse cumulative computation
* @since 2.1
*/
private double solverAbsoluteAccuracy = BrentSolver.DEFAULT_ABSOLUTE_ACCURACY;
/**
* Default constructor.
*/
protected AbstractContinuousDistribution() {
super();
}
/**
* Return the probability density for a particular point.
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @throws MathRuntimeException if the specialized class hasn't implemented this function
* @since 2.1
*/
public double density(double x) throws MathRuntimeException {
throw new MathRuntimeException(new UnsupportedOperationException(),
LocalizedFormats.NO_DENSITY_FOR_THIS_DISTRIBUTION);
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X < x) = <code>p</code>.
*
* @param p the desired probability
* @return x, such that P(X < x) = <code>p</code>
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if <code>p</code> is not a valid
* probability.
*/
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
}
// by default, do simple root finding using bracketing and default solver.
// subclasses can override if there is a better method.
UnivariateRealFunction rootFindingFunction =
new UnivariateRealFunction() {
public double value(double x) throws FunctionEvaluationException {
double ret = Double.NaN;
try {
ret = cumulativeProbability(x) - p;
} catch (MathException ex) {
throw new FunctionEvaluationException(x, ex.getSpecificPattern(), ex.getGeneralPattern(), ex.getArguments());
}
if (Double.isNaN(ret)) {
throw new FunctionEvaluationException(x, LocalizedFormats.CUMULATIVE_PROBABILITY_RETURNED_NAN, x, p);
}
return ret;
}
};
// Try to bracket root, test domain endpoints if this fails
double lowerBound = getDomainLowerBound(p);
double upperBound = getDomainUpperBound(p);
double[] bracket = null;
try {
bracket = UnivariateRealSolverUtils.bracket(
rootFindingFunction, getInitialDomain(p),
lowerBound, upperBound);
} catch (ConvergenceException ex) {
/*
* Check domain endpoints to see if one gives value that is within
* the default solver's defaultAbsoluteAccuracy of 0 (will be the
* case if density has bounded support and p is 0 or 1).
*/
if (FastMath.abs(rootFindingFunction.value(lowerBound)) < getSolverAbsoluteAccuracy()) {
return lowerBound;
}
if (FastMath.abs(rootFindingFunction.value(upperBound)) < getSolverAbsoluteAccuracy()) {
return upperBound;
}
// Failed bracket convergence was not because of corner solution
throw new MathException(ex);
}
// find root
double root = UnivariateRealSolverUtils.solve(rootFindingFunction,
// override getSolverAbsoluteAccuracy() to use a Brent solver with
// absolute accuracy different from BrentSolver default
bracket[0],bracket[1], getSolverAbsoluteAccuracy());
return root;
}
/**
* Reseeds the random generator used to generate samples.
*
* @param seed the new seed
* @since 2.2
*/
public void reseedRandomGenerator(long seed) {
randomData.reSeed(seed);
}
/**
* Generates a random value sampled from this distribution. The default
* implementation uses the
* <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> inversion method.</a>
*
* @return random value
* @since 2.2
* @throws MathException if an error occurs generating the random value
*/
public double sample() throws MathException {
return randomData.nextInversionDeviate(this);
}
/**
* Generates a random sample from the distribution. The default implementation
* generates the sample by calling {@link #sample()} in a loop.
*
* @param sampleSize number of random values to generate
* @since 2.2
* @return an array representing the random sample
* @throws MathException if an error occurs generating the sample
* @throws IllegalArgumentException if sampleSize is not positive
*/
public double[] sample(int sampleSize) throws MathException {
if (sampleSize <= 0) {
MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, sampleSize);
}
double[] out = new double[sampleSize];
for (int i = 0; i < sampleSize; i++) {
out[i] = sample();
}
return out;
}
/**
* Access the initial domain value, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
protected abstract double getInitialDomain(double p);
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < <i>lower bound</i>) < <code>p</code>
*/
protected abstract double getDomainLowerBound(double p);
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < <i>upper bound</i>) > <code>p</code>
*/
protected abstract double getDomainUpperBound(double p);
/**
* Returns the solver absolute accuracy for inverse cumulative computation.
*
* @return the maximum absolute error in inverse cumulative probability estimates
* @since 2.1
*/
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
}