org.apache.commons.numbers.gamma.RegularizedBeta Maven / Gradle / Ivy
/*
* 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 org.apache.commons.numbers.fraction.ContinuedFraction;
/**
*
* Regularized Beta function.
*
* This class is immutable.
*
*/
public final class RegularizedBeta {
/** Maximum allowed numerical error. */
private static final double DEFAULT_EPSILON = 1e-14;
/** Private constructor. */
private RegularizedBeta() {
// intentionally empty.
}
/**
* Computes the value of the
*
* regularized beta function I(x, a, b).
*
* @param x Value.
* @param a Parameter {@code a}.
* @param b Parameter {@code b}.
* @return the regularized beta function I(x, a, b).
* @throws ArithmeticException if the algorithm fails to converge.
*/
public static double value(double x,
double a,
double b) {
return value(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Computes the value of the
*
* regularized beta function I(x, a, b).
*
* The implementation of this method is based on:
*
* -
*
* Regularized Beta Function.
*
* -
*
* Regularized Beta Function.
*
*
*
* @param x the value.
* @param a Parameter {@code a}.
* @param b Parameter {@code b}.
* @param epsilon When the absolute value of the nth item in the
* series is less than epsilon the approximation ceases to calculate
* further elements in the series.
* @param maxIterations Maximum number of "iterations" to complete.
* @return the regularized beta function I(x, a, b).
* @throws ArithmeticException if the algorithm fails to converge.
*/
public static double value(double x,
final double a,
final double b,
double epsilon,
int maxIterations) {
if (Double.isNaN(x) ||
Double.isNaN(a) ||
Double.isNaN(b) ||
x < 0 ||
x > 1 ||
a <= 0 ||
b <= 0) {
return Double.NaN;
} else if (x > (a + 1) / (2 + b + a) &&
1 - x <= (b + 1) / (2 + b + a)) {
return 1 - value(1 - x, b, a, epsilon, maxIterations);
} else {
final ContinuedFraction fraction = new ContinuedFraction() {
/** {@inheritDoc} */
@Override
protected double getA(int n, double x) {
if (n % 2 == 0) { // even
final double m = n / 2d;
return (m * (b - m) * x) /
((a + (2 * m) - 1) * (a + (2 * m)));
} else {
final double m = (n - 1d) / 2d;
return -((a + m) * (a + b + m) * x) /
((a + (2 * m)) * (a + (2 * m) + 1));
}
}
/** {@inheritDoc} */
@Override
protected double getB(int n, double x) {
return 1;
}
};
return Math.exp((a * Math.log(x)) + (b * Math.log1p(-x)) -
Math.log(a) - LogBeta.value(a, b)) /
fraction.evaluate(x, epsilon, maxIterations);
}
}
}