diff options
Diffstat (limited to 'src/main/java/org/apache/commons/math/special/Beta.java')
-rw-r--r-- | src/main/java/org/apache/commons/math/special/Beta.java | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/special/Beta.java b/src/main/java/org/apache/commons/math/special/Beta.java new file mode 100644 index 0000000..6ab284f --- /dev/null +++ b/src/main/java/org/apache/commons/math/special/Beta.java @@ -0,0 +1,202 @@ +/* + * 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.special; + +import org.apache.commons.math.MathException; +import org.apache.commons.math.util.ContinuedFraction; +import org.apache.commons.math.util.FastMath; + +/** + * This is a utility class that provides computation methods related to the + * Beta family of functions. + * + * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ + */ +public class Beta { + + /** Maximum allowed numerical error. */ + private static final double DEFAULT_EPSILON = 10e-15; + + /** + * Default constructor. Prohibit instantiation. + */ + private Beta() { + super(); + } + + /** + * Returns the + * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> + * regularized beta function</a> I(x, a, b). + * + * @param x the value. + * @param a the a parameter. + * @param b the b parameter. + * @return the regularized beta function I(x, a, b) + * @throws MathException if the algorithm fails to converge. + */ + public static double regularizedBeta(double x, double a, double b) + throws MathException + { + return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE); + } + + /** + * Returns the + * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> + * regularized beta function</a> I(x, a, b). + * + * @param x the value. + * @param a the a parameter. + * @param b the b parameter. + * @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. + * @return the regularized beta function I(x, a, b) + * @throws MathException if the algorithm fails to converge. + */ + public static double regularizedBeta(double x, double a, double b, + double epsilon) throws MathException + { + return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE); + } + + /** + * Returns the regularized beta function I(x, a, b). + * + * @param x the value. + * @param a the a parameter. + * @param b the b parameter. + * @param maxIterations Maximum number of "iterations" to complete. + * @return the regularized beta function I(x, a, b) + * @throws MathException if the algorithm fails to converge. + */ + public static double regularizedBeta(double x, double a, double b, + int maxIterations) throws MathException + { + return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations); + } + + /** + * Returns the regularized beta function I(x, a, b). + * + * The implementation of this method is based on: + * <ul> + * <li> + * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> + * Regularized Beta Function</a>.</li> + * <li> + * <a href="http://functions.wolfram.com/06.21.10.0001.01"> + * Regularized Beta Function</a>.</li> + * </ul> + * + * @param x the value. + * @param a the a parameter. + * @param b the b parameter. + * @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 MathException if the algorithm fails to converge. + */ + public static double regularizedBeta(double x, final double a, + final double b, double epsilon, int maxIterations) throws MathException + { + double ret; + + if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b) || (x < 0) || + (x > 1) || (a <= 0.0) || (b <= 0.0)) + { + ret = Double.NaN; + } else if (x > (a + 1.0) / (a + b + 2.0)) { + ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations); + } else { + ContinuedFraction fraction = new ContinuedFraction() { + + @Override + protected double getB(int n, double x) { + double ret; + double m; + if (n % 2 == 0) { // even + m = n / 2.0; + ret = (m * (b - m) * x) / + ((a + (2 * m) - 1) * (a + (2 * m))); + } else { + m = (n - 1.0) / 2.0; + ret = -((a + m) * (a + b + m) * x) / + ((a + (2 * m)) * (a + (2 * m) + 1.0)); + } + return ret; + } + + @Override + protected double getA(int n, double x) { + return 1.0; + } + }; + ret = FastMath.exp((a * FastMath.log(x)) + (b * FastMath.log(1.0 - x)) - + FastMath.log(a) - logBeta(a, b, epsilon, maxIterations)) * + 1.0 / fraction.evaluate(x, epsilon, maxIterations); + } + + return ret; + } + + /** + * Returns the natural logarithm of the beta function B(a, b). + * + * @param a the a parameter. + * @param b the b parameter. + * @return log(B(a, b)) + */ + public static double logBeta(double a, double b) { + return logBeta(a, b, DEFAULT_EPSILON, Integer.MAX_VALUE); + } + + /** + * Returns the natural logarithm of the beta function B(a, b). + * + * The implementation of this method is based on: + * <ul> + * <li><a href="http://mathworld.wolfram.com/BetaFunction.html"> + * Beta Function</a>, equation (1).</li> + * </ul> + * + * @param a the a parameter. + * @param b the b parameter. + * @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 log(B(a, b)) + */ + public static double logBeta(double a, double b, double epsilon, + int maxIterations) { + + double ret; + + if (Double.isNaN(a) || Double.isNaN(b) || (a <= 0.0) || (b <= 0.0)) { + ret = Double.NaN; + } else { + ret = Gamma.logGamma(a) + Gamma.logGamma(b) - + Gamma.logGamma(a + b); + } + + return ret; + } +} |