/*
* 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.math4.distribution;
import java.io.Serializable;
import org.apache.commons.math4.exception.MathInternalError;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.sampling.distribution.InverseTransformDiscreteSampler;
import org.apache.commons.rng.sampling.distribution.DiscreteInverseCumulativeProbabilityFunction;
import org.apache.commons.rng.sampling.distribution.DiscreteSampler;
import org.apache.commons.math4.util.FastMath;
/**
* Base class for integer-valued discrete distributions. Default
* implementations are provided for some of the methods that do not vary
* from distribution to distribution.
*
*/
public abstract class AbstractIntegerDistribution implements IntegerDistribution, Serializable {
/** Serializable version identifier */
private static final long serialVersionUID = 20160318L;
/**
* {@inheritDoc}
*
* The default implementation uses the identity
* <p>{@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}</p>
*
* @since 4.0, was previously named cumulativeProbability
*/
@Override
public double probability(int x0, int x1) throws NumberIsTooLargeException {
if (x1 < x0) {
throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
x0, x1, true);
}
return cumulativeProbability(x1) - cumulativeProbability(x0);
}
/**
* {@inheritDoc}
*
* The default implementation returns
* <ul>
* <li>{@link #getSupportLowerBound()} for {@code p = 0},</li>
* <li>{@link #getSupportUpperBound()} for {@code p = 1}, and</li>
* <li>{@link #solveInverseCumulativeProbability(double, int, int)} for
* {@code 0 < p < 1}.</li>
* </ul>
*/
@Override
public int inverseCumulativeProbability(final double p) throws OutOfRangeException {
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(p, 0, 1);
}
int lower = getSupportLowerBound();
if (p == 0.0) {
return lower;
}
if (lower == Integer.MIN_VALUE) {
if (checkedCumulativeProbability(lower) >= p) {
return lower;
}
} else {
lower -= 1; // this ensures cumulativeProbability(lower) < p, which
// is important for the solving step
}
int upper = getSupportUpperBound();
if (p == 1.0) {
return upper;
}
// use the one-sided Chebyshev inequality to narrow the bracket
// cf. AbstractRealDistribution.inverseCumulativeProbability(double)
final double mu = getNumericalMean();
final double sigma = FastMath.sqrt(getNumericalVariance());
final boolean chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) ||
Double.isInfinite(sigma) || Double.isNaN(sigma) || sigma == 0.0);
if (chebyshevApplies) {
double k = FastMath.sqrt((1.0 - p) / p);
double tmp = mu - k * sigma;
if (tmp > lower) {
lower = ((int) FastMath.ceil(tmp)) - 1;
}
k = 1.0 / k;
tmp = mu + k * sigma;
if (tmp < upper) {
upper = ((int) FastMath.ceil(tmp)) - 1;
}
}
return solveInverseCumulativeProbability(p, lower, upper);
}
/**
* This is a utility function used by {@link
* #inverseCumulativeProbability(double)}. It assumes {@code 0 < p < 1} and
* that the inverse cumulative probability lies in the bracket {@code
* (lower, upper]}. The implementation does simple bisection to find the
* smallest {@code p}-quantile {@code inf{x in Z | P(X<=x) >= p}}.
*
* @param p the cumulative probability
* @param lower a value satisfying {@code cumulativeProbability(lower) < p}
* @param upper a value satisfying {@code p <= cumulativeProbability(upper)}
* @return the smallest {@code p}-quantile of this distribution
*/
protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {
while (lower + 1 < upper) {
int xm = (lower + upper) / 2;
if (xm < lower || xm > upper) {
/*
* Overflow.
* There will never be an overflow in both calculation methods
* for xm at the same time
*/
xm = lower + (upper - lower) / 2;
}
double pm = checkedCumulativeProbability(xm);
if (pm >= p) {
upper = xm;
} else {
lower = xm;
}
}
return upper;
}
/**
* Computes the cumulative probability function and checks for {@code NaN}
* values returned. Throws {@code MathInternalError} if the value is
* {@code NaN}. Rethrows any exception encountered evaluating the cumulative
* probability function. Throws {@code MathInternalError} if the cumulative
* probability function returns {@code NaN}.
*
* @param argument input value
* @return the cumulative probability
* @throws MathInternalError if the cumulative probability is {@code NaN}
*/
private double checkedCumulativeProbability(int argument)
throws MathInternalError {
final double result = cumulativeProbability(argument);
if (Double.isNaN(result)) {
throw new MathInternalError(LocalizedFormats
.DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);
}
return result;
}
/**
* {@inheritDoc}
* <p>
* The default implementation simply computes the logarithm of {@code probability(x)}.
*/
@Override
public double logProbability(int x) {
return FastMath.log(probability(x));
}
/**
* Utility function for allocating an array and filling it with {@code n}
* samples generated by the given {@code sampler}.
*
* @param n Number of samples.
* @param sampler Sampler.
* @return an array of size {@code n}.
*/
public static int[] sample(int n,
IntegerDistribution.Sampler sampler) {
final int[] samples = new int[n];
for (int i = 0; i < n; i++) {
samples[i] = sampler.sample();
}
return samples;
}
/**{@inheritDoc} */
@Override
public IntegerDistribution.Sampler createSampler(final UniformRandomProvider rng) {
return new IntegerDistribution.Sampler() {
/**
* Inversion method distribution sampler.
*/
private final DiscreteSampler sampler =
new InverseTransformDiscreteSampler(rng, createICPF());
/** {@inheritDoc} */
@Override
public int sample() {
return sampler.sample();
}
};
}
/**
* @return an instance for use by {@link #createSampler(UniformRandomProvider)}
*/
private DiscreteInverseCumulativeProbabilityFunction createICPF() {
return new DiscreteInverseCumulativeProbabilityFunction() {
/** {@inheritDoc} */
@Override
public int inverseCumulativeProbability(double p) {
return AbstractIntegerDistribution.this.inverseCumulativeProbability(p);
}
};
}
}