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* 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.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.ResizableDoubleArray;
/**
* Implementation of the exponential distribution.
*
* @see Exponential distribution (Wikipedia)
* @see Exponential distribution (MathWorld)
*/
public class ExponentialDistribution extends AbstractRealDistribution {
/**
* Default inverse cumulative probability accuracy.
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/** Serializable version identifier */
private static final long serialVersionUID = 2401296428283614780L;
/**
* Used when generating Exponential samples.
* Table containing the constants
* q_i = sum_{j=1}^i (ln 2)^j/j! = ln 2 + (ln 2)^2/2 + ... + (ln 2)^i/i!
* until the largest representable fraction below 1 is exceeded.
*
* Note that
* 1 = 2 - 1 = exp(ln 2) - 1 = sum_{n=1}^infty (ln 2)^n / n!
* thus q_i -> 1 as i -> +inf,
* so the higher i, the closer to one we get (the series is not alternating).
*
* By trying, n = 16 in Java is enough to reach 1.0.
*/
private static final double[] EXPONENTIAL_SA_QI;
/** The mean of this distribution. */
private final double mean;
/** The logarithm of the mean, stored to reduce computing time. **/
private final double logMean;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/**
* Initialize tables.
*/
static {
/**
* Filling EXPONENTIAL_SA_QI table.
* Note that we don't want qi = 0 in the table.
*/
final double LN2 = FastMath.log(2);
double qi = 0;
int i = 1;
/**
* ArithmeticUtils provides factorials up to 20, so let's use that
* limit together with Precision.EPSILON to generate the following
* code (a priori, we know that there will be 16 elements, but it is
* better to not hardcode it).
*/
final ResizableDoubleArray ra = new ResizableDoubleArray(20);
while (qi < 1) {
qi += FastMath.pow(LN2, i) / CombinatoricsUtils.factorial(i);
ra.addElement(qi);
++i;
}
EXPONENTIAL_SA_QI = ra.getElements();
}
/**
* Create an exponential distribution with the given mean.
*
* Note: this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param mean mean of this distribution.
*/
public ExponentialDistribution(double mean) {
this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create an exponential distribution with the given mean.
*
* Note: this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param mean Mean of this distribution.
* @param inverseCumAccuracy Maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code mean <= 0}.
* @since 2.1
*/
public ExponentialDistribution(double mean, double inverseCumAccuracy) {
this(new Well19937c(), mean, inverseCumAccuracy);
}
/**
* Creates an exponential distribution.
*
* @param rng Random number generator.
* @param mean Mean of this distribution.
* @throws NotStrictlyPositiveException if {@code mean <= 0}.
* @since 3.3
*/
public ExponentialDistribution(RandomGenerator rng, double mean)
throws NotStrictlyPositiveException {
this(rng, mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates an exponential distribution.
*
* @param rng Random number generator.
* @param mean Mean of this distribution.
* @param inverseCumAccuracy Maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code mean <= 0}.
* @since 3.1
*/
public ExponentialDistribution(RandomGenerator rng,
double mean,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (mean <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);
}
this.mean = mean;
logMean = FastMath.log(mean);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the mean.
*
* @return the mean.
*/
public double getMean() {
return mean;
}
/** {@inheritDoc} */
public double density(double x) {
final double logDensity = logDensity(x);
return logDensity == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logDensity);
}
/** {@inheritDoc} **/
@Override
public double logDensity(double x) {
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
return -x / mean - logMean;
}
/**
* {@inheritDoc}
*
* The implementation of this method is based on:
*
* -
*
* Exponential Distribution, equation (1).
*
*/
public double cumulativeProbability(double x) {
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = 1.0 - FastMath.exp(-x / mean);
}
return ret;
}
/**
* {@inheritDoc}
*
* Returns {@code 0} when {@code p= = 0} and
* {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
double ret;
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0.0, 1.0);
} else if (p == 1.0) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = -mean * FastMath.log(1.0 - p);
}
return ret;
}
/**
* {@inheritDoc}
*
* Algorithm Description: this implementation uses the
*
* Inversion Method to generate exponentially distributed random values
* from uniform deviates.
*
* @return a random value.
* @since 2.2
*/
@Override
public double sample() {
// Step 1:
double a = 0;
double u = random.nextDouble();
// Step 2 and 3:
while (u < 0.5) {
a += EXPONENTIAL_SA_QI[0];
u *= 2;
}
// Step 4 (now u >= 0.5):
u += u - 1;
// Step 5:
if (u <= EXPONENTIAL_SA_QI[0]) {
return mean * (a + u);
}
// Step 6:
int i = 0; // Should be 1, be we iterate before it in while using 0
double u2 = random.nextDouble();
double umin = u2;
// Step 7 and 8:
do {
++i;
u2 = random.nextDouble();
if (u2 < umin) {
umin = u2;
}
// Step 8:
} while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1
return mean * (a + umin * EXPONENTIAL_SA_QI[0]);
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the mean is {@code k}.
*/
public double getNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the variance is {@code k^2}.
*/
public double getNumericalVariance() {
final double m = getMean();
return m * m;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the mean parameter.
*
* @return lower bound of the support (always 0)
*/
public double getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the mean parameter.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return true;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}