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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.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;
+    }
+}