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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.numbers.gamma;
import java.text.MessageFormat;
import org.apache.commons.numbers.fraction.ContinuedFraction;
/**
*
* Regularized Gamma functions.
*
* Class is immutable.
*/
public final class RegularizedGamma {
/** Maximum allowed numerical error. */
private static final double DEFAULT_EPSILON = 1e-15;
/** Private constructor. */
private RegularizedGamma() {
// intentionally empty.
}
/**
* \( P(a, x) \)
* regularized Gamma function.
*
* Class is immutable.
*/
public static final class P {
/** Prevent instantiation. */
private P() {}
/**
* Computes the regularized gamma function \( P(a, x) \).
*
* @param a Argument.
* @param x Argument.
* @return \( P(a, x) \).
* @throws ArithmeticException if the continued fraction fails to converge.
*/
public static double value(double a,
double x) {
return value(a, x, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Computes the regularized gamma function \( P(a, x) \).
*
* The implementation of this method is based on:
*
*
* @param a Argument.
* @param x Argument.
* @param epsilon Tolerance in continued fraction evaluation.
* @param maxIterations Maximum number of iterations in continued fraction evaluation.
* @return \( P(a, x) \).
* @throws ArithmeticException if the continued fraction fails to converge.
*/
public static double value(double a,
double x,
double epsilon,
int maxIterations) {
if (Double.isNaN(a) ||
Double.isNaN(x) ||
a <= 0 ||
x < 0) {
return Double.NaN;
} else if (x == 0) {
return 0;
} else if (x >= a + 1) {
// Q should converge faster in this case.
return 1 - RegularizedGamma.Q.value(a, x, epsilon, maxIterations);
} else {
// Series.
double n = 0; // current element index
double an = 1 / a; // n-th element in the series
double sum = an; // partial sum
while (Math.abs(an / sum) > epsilon &&
n < maxIterations &&
sum < Double.POSITIVE_INFINITY) {
// compute next element in the series
n += 1;
an *= x / (a + n);
// update partial sum
sum += an;
}
if (n >= maxIterations) {
throw new ArithmeticException(
MessageFormat.format("Failed to converge within {0} iterations", maxIterations));
} else if (Double.isInfinite(sum)) {
return 1;
} else {
// Ensure result is in the range [0, 1]
final double result = Math.exp(-x + (a * Math.log(x)) - LogGamma.value(a)) * sum;
return result > 1.0 ? 1.0 : result;
}
}
}
}
/**
* Creates the \( Q(a, x) \equiv 1 - P(a, x) \)
* regularized Gamma function.
*
* Class is immutable.
*/
public static final class Q {
/** Prevent instantiation. */
private Q() {}
/**
* Computes the regularized gamma function \( Q(a, x) = 1 - P(a, x) \).
*
* @param a Argument.
* @param x Argument.
* @return \( Q(a, x) \).
* @throws ArithmeticException if the continued fraction fails to converge.
*/
public static double value(double a,
double x) {
return value(a, x, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Computes the regularized gamma function \( Q(a, x) = 1 - P(a, x) \).
*
* The implementation of this method is based on:
*
