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Java example source code file (BetaTest.java)

This example Java source code file (BetaTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

class, double, illegalaccessexception, invocationtargetexception, log_gamma_minus_log_gamma_sum_method, log_gamma_minus_log_gamma_sum_ref, mathillegalargumentexception, method, nosuchmethodexception, reflection, stringbuilder, sum_delta_minus_delta_sum_method, sum_delta_minus_delta_sum_ref, test, throwable

The BetaTest.java Java example source code

/*
 * 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.math3.special;

import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 */
public class BetaTest {

    /*
     * Use reflection to test private methods.
     */
    private static final Method LOG_GAMMA_SUM_METHOD;

    private static final Method LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD;

    private static final Method SUM_DELTA_MINUS_DELTA_SUM_METHOD;

    static {
        final Class<Beta> b;
        final Class<Double> d = Double.TYPE;
        b = Beta.class;
        Method m = null;
        try {
            m = b.getDeclaredMethod("logGammaSum", d, d);
        } catch (NoSuchMethodException e) {
            Assert.fail(e.getMessage());
        }
        LOG_GAMMA_SUM_METHOD = m;
        LOG_GAMMA_SUM_METHOD.setAccessible(true);

        m = null;
        try {
            m = b.getDeclaredMethod("logGammaMinusLogGammaSum",d, d);
        } catch (NoSuchMethodException e) {
            Assert.fail(e.getMessage());
        }
        LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD = m;
        LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD.setAccessible(true);

        m = null;
        try {
            m = b.getDeclaredMethod("sumDeltaMinusDeltaSum",d, d);
        } catch (NoSuchMethodException e) {
            Assert.fail(e.getMessage());
        }
        SUM_DELTA_MINUS_DELTA_SUM_METHOD = m;
        SUM_DELTA_MINUS_DELTA_SUM_METHOD.setAccessible(true);
    }

    private void testRegularizedBeta(double expected, double x,
                                     double a, double b) {
        double actual = Beta.regularizedBeta(x, a, b);
        TestUtils.assertEquals(expected, actual, 10e-15);
    }

    private void testLogBeta(double expected, double a, double b) {
        double actual = Beta.logBeta(a, b);
        TestUtils.assertEquals(expected, actual, 10e-15);
    }

    @Test
    public void testRegularizedBetaNanPositivePositive() {
        testRegularizedBeta(Double.NaN, Double.NaN, 1.0, 1.0);
    }

    @Test
    public void testRegularizedBetaPositiveNanPositive() {
        testRegularizedBeta(Double.NaN, 0.5, Double.NaN, 1.0);
    }

    @Test
    public void testRegularizedBetaPositivePositiveNan() {
        testRegularizedBeta(Double.NaN, 0.5, 1.0, Double.NaN);
    }

    @Test
    public void testRegularizedBetaNegativePositivePositive() {
        testRegularizedBeta(Double.NaN, -0.5, 1.0, 2.0);
    }

    @Test
    public void testRegularizedBetaPositiveNegativePositive() {
        testRegularizedBeta(Double.NaN, 0.5, -1.0, 2.0);
    }

    @Test
    public void testRegularizedBetaPositivePositiveNegative() {
        testRegularizedBeta(Double.NaN, 0.5, 1.0, -2.0);
    }

    @Test
    public void testRegularizedBetaZeroPositivePositive() {
        testRegularizedBeta(0.0, 0.0, 1.0, 2.0);
    }

    @Test
    public void testRegularizedBetaPositiveZeroPositive() {
        testRegularizedBeta(Double.NaN, 0.5, 0.0, 2.0);
    }

    @Test
    public void testRegularizedBetaPositivePositiveZero() {
        testRegularizedBeta(Double.NaN, 0.5, 1.0, 0.0);
    }

    @Test
    public void testRegularizedBetaPositivePositivePositive() {
        testRegularizedBeta(0.75, 0.5, 1.0, 2.0);
    }

    @Test
    public void testRegularizedBetaTinyArgument() {
        double actual = Beta.regularizedBeta(1e-17, 1.0, 1e12);
        // This value is from R: pbeta(1e-17,1,1e12)
        TestUtils.assertEquals(9.999950000166648e-6, actual, 1e-16);
    }

    @Test
    public void testMath1067() {
        final double x = 0.22580645161290325;
        final double a = 64.33333333333334;
        final double b = 223;

        try {
            Beta.regularizedBeta(x, a, b, 1e-14, 10000);
        } catch (StackOverflowError error) {
            Assert.fail("Infinite recursion");
        }
    }

    @Test
    public void testLogBetaNanPositive() {
        testLogBeta(Double.NaN, Double.NaN, 2.0);
    }

    @Test
    public void testLogBetaPositiveNan() {
        testLogBeta(Double.NaN, 1.0, Double.NaN);
    }

    @Test
    public void testLogBetaNegativePositive() {
        testLogBeta(Double.NaN, -1.0, 2.0);
    }

    @Test
    public void testLogBetaPositiveNegative() {
        testLogBeta(Double.NaN, 1.0, -2.0);
    }

    @Test
    public void testLogBetaZeroPositive() {
        testLogBeta(Double.NaN, 0.0, 2.0);
    }

    @Test
    public void testLogBetaPositiveZero() {
        testLogBeta(Double.NaN, 1.0, 0.0);
    }

    @Test
    public void testLogBetaPositivePositive() {
        testLogBeta(-0.693147180559945, 1.0, 2.0);
    }

    /**
     * Reference data for the {@link #logGammaSum(double, double)}
     * function. This data was generated with the following
     * <a href="http://maxima.sourceforge.net/">Maxima script.
     *
     * <pre>
     * kill(all);
     *
     * fpprec : 64;
     * gsumln(a, b) := log(gamma(a + b));
     *
     * x : [1.0b0, 1.125b0, 1.25b0, 1.375b0, 1.5b0, 1.625b0, 1.75b0, 1.875b0, 2.0b0];
     *
     * for i : 1 while i <= length(x) do
     *   for j : 1 while j <= length(x) do block(
     *     a : x[i],
     *     b : x[j],
     *     print("{", float(a), ",", float(b), ",", float(gsumln(a, b)), "},")
     *   );
     * </pre>
     */
    private static final double[][] LOG_GAMMA_SUM_REF = {
        { 1.0 , 1.0 , 0.0 },
        { 1.0 , 1.125 , .05775985153034387 },
        { 1.0 , 1.25 , .1248717148923966 },
        { 1.0 , 1.375 , .2006984603774558 },
        { 1.0 , 1.5 , .2846828704729192 },
        { 1.0 , 1.625 , .3763336820249054 },
        { 1.0 , 1.75 , .4752146669149371 },
        { 1.0 , 1.875 , .5809359740231859 },
        { 1.0 , 2.0 , .6931471805599453 },
        { 1.125 , 1.0 , .05775985153034387 },
        { 1.125 , 1.125 , .1248717148923966 },
        { 1.125 , 1.25 , .2006984603774558 },
        { 1.125 , 1.375 , .2846828704729192 },
        { 1.125 , 1.5 , .3763336820249054 },
        { 1.125 , 1.625 , .4752146669149371 },
        { 1.125 , 1.75 , .5809359740231859 },
        { 1.125 , 1.875 , .6931471805599453 },
        { 1.125 , 2.0 , 0.811531653906724 },
        { 1.25 , 1.0 , .1248717148923966 },
        { 1.25 , 1.125 , .2006984603774558 },
        { 1.25 , 1.25 , .2846828704729192 },
        { 1.25 , 1.375 , .3763336820249054 },
        { 1.25 , 1.5 , .4752146669149371 },
        { 1.25 , 1.625 , .5809359740231859 },
        { 1.25 , 1.75 , .6931471805599453 },
        { 1.25 , 1.875 , 0.811531653906724 },
        { 1.25 , 2.0 , .9358019311087253 },
        { 1.375 , 1.0 , .2006984603774558 },
        { 1.375 , 1.125 , .2846828704729192 },
        { 1.375 , 1.25 , .3763336820249054 },
        { 1.375 , 1.375 , .4752146669149371 },
        { 1.375 , 1.5 , .5809359740231859 },
        { 1.375 , 1.625 , .6931471805599453 },
        { 1.375 , 1.75 , 0.811531653906724 },
        { 1.375 , 1.875 , .9358019311087253 },
        { 1.375 , 2.0 , 1.06569589786406 },
        { 1.5 , 1.0 , .2846828704729192 },
        { 1.5 , 1.125 , .3763336820249054 },
        { 1.5 , 1.25 , .4752146669149371 },
        { 1.5 , 1.375 , .5809359740231859 },
        { 1.5 , 1.5 , .6931471805599453 },
        { 1.5 , 1.625 , 0.811531653906724 },
        { 1.5 , 1.75 , .9358019311087253 },
        { 1.5 , 1.875 , 1.06569589786406 },
        { 1.5 , 2.0 , 1.200973602347074 },
        { 1.625 , 1.0 , .3763336820249054 },
        { 1.625 , 1.125 , .4752146669149371 },
        { 1.625 , 1.25 , .5809359740231859 },
        { 1.625 , 1.375 , .6931471805599453 },
        { 1.625 , 1.5 , 0.811531653906724 },
        { 1.625 , 1.625 , .9358019311087253 },
        { 1.625 , 1.75 , 1.06569589786406 },
        { 1.625 , 1.875 , 1.200973602347074 },
        { 1.625 , 2.0 , 1.341414578068493 },
        { 1.75 , 1.0 , .4752146669149371 },
        { 1.75 , 1.125 , .5809359740231859 },
        { 1.75 , 1.25 , .6931471805599453 },
        { 1.75 , 1.375 , 0.811531653906724 },
        { 1.75 , 1.5 , .9358019311087253 },
        { 1.75 , 1.625 , 1.06569589786406 },
        { 1.75 , 1.75 , 1.200973602347074 },
        { 1.75 , 1.875 , 1.341414578068493 },
        { 1.75 , 2.0 , 1.486815578593417 },
        { 1.875 , 1.0 , .5809359740231859 },
        { 1.875 , 1.125 , .6931471805599453 },
        { 1.875 , 1.25 , 0.811531653906724 },
        { 1.875 , 1.375 , .9358019311087253 },
        { 1.875 , 1.5 , 1.06569589786406 },
        { 1.875 , 1.625 , 1.200973602347074 },
        { 1.875 , 1.75 , 1.341414578068493 },
        { 1.875 , 1.875 , 1.486815578593417 },
        { 1.875 , 2.0 , 1.6369886482725 },
        { 2.0 , 1.0 , .6931471805599453 },
        { 2.0 , 1.125 , 0.811531653906724 },
        { 2.0 , 1.25 , .9358019311087253 },
        { 2.0 , 1.375 , 1.06569589786406 },
        { 2.0 , 1.5 , 1.200973602347074 },
        { 2.0 , 1.625 , 1.341414578068493 },
        { 2.0 , 1.75 , 1.486815578593417 },
        { 2.0 , 1.875 , 1.6369886482725 },
        { 2.0 , 2.0 , 1.791759469228055 },
    };

    private static double logGammaSum(final double a, final double b) {

        /*
         * Use reflection to access private method.
         */
        try {
            return ((Double) LOG_GAMMA_SUM_METHOD.invoke(null, a, b)).doubleValue();
        } catch (final IllegalAccessException e) {
            Assert.fail(e.getMessage());
        } catch (final IllegalArgumentException e) {
            Assert.fail(e.getMessage());
        } catch (final InvocationTargetException e) {
            final Throwable te = e.getTargetException();
            if (te instanceof MathIllegalArgumentException) {
                throw (MathIllegalArgumentException) te;
            }
            Assert.fail(e.getMessage());
        }
        return Double.NaN;
    }

    @Test
    public void testLogGammaSum() {
        final int ulps = 2;
        for (int i = 0; i < LOG_GAMMA_SUM_REF.length; i++) {
            final double[] ref = LOG_GAMMA_SUM_REF[i];
            final double a = ref[0];
            final double b = ref[1];
            final double expected = ref[2];
            final double actual = logGammaSum(a, b);
            final double tol = ulps * FastMath.ulp(expected);
            final StringBuilder builder = new StringBuilder();
            builder.append(a).append(", ").append(b);
            Assert.assertEquals(builder.toString(), expected, actual, tol);
        }
    }

    @Test(expected = OutOfRangeException.class)
    public void testLogGammaSumPrecondition1() {

        logGammaSum(0.0, 1.0);
    }

    @Test(expected = OutOfRangeException.class)
    public void testLogGammaSumPrecondition2() {

        logGammaSum(3.0, 1.0);
    }

    @Test(expected = OutOfRangeException.class)
    public void testLogGammaSumPrecondition3() {

        logGammaSum(1.0, 0.0);
    }

    @Test(expected = OutOfRangeException.class)
    public void testLogGammaSumPrecondition4() {

        logGammaSum(1.0, 3.0);
    }

    private static final double[][] LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF = {
//        { 0.0 , 8.0 , 0.0 },
//        { 0.0 , 9.0 , 0.0 },
        { 0.0 , 10.0 , 0.0 },
        { 0.0 , 11.0 , 0.0 },
        { 0.0 , 12.0 , 0.0 },
        { 0.0 , 13.0 , 0.0 },
        { 0.0 , 14.0 , 0.0 },
        { 0.0 , 15.0 , 0.0 },
        { 0.0 , 16.0 , 0.0 },
        { 0.0 , 17.0 , 0.0 },
        { 0.0 , 18.0 , 0.0 },
//        { 1.0 , 8.0 , - 2.079441541679836 },
//        { 1.0 , 9.0 , - 2.19722457733622 },
        { 1.0 , 10.0 , - 2.302585092994046 },
        { 1.0 , 11.0 , - 2.397895272798371 },
        { 1.0 , 12.0 , - 2.484906649788 },
        { 1.0 , 13.0 , - 2.564949357461537 },
        { 1.0 , 14.0 , - 2.639057329615258 },
        { 1.0 , 15.0 , - 2.70805020110221 },
        { 1.0 , 16.0 , - 2.772588722239781 },
        { 1.0 , 17.0 , - 2.833213344056216 },
        { 1.0 , 18.0 , - 2.890371757896165 },
//        { 2.0 , 8.0 , - 4.276666119016055 },
//        { 2.0 , 9.0 , - 4.499809670330265 },
        { 2.0 , 10.0 , - 4.700480365792417 },
        { 2.0 , 11.0 , - 4.882801922586371 },
        { 2.0 , 12.0 , - 5.049856007249537 },
        { 2.0 , 13.0 , - 5.204006687076795 },
        { 2.0 , 14.0 , - 5.347107530717468 },
        { 2.0 , 15.0 , - 5.480638923341991 },
        { 2.0 , 16.0 , - 5.605802066295998 },
        { 2.0 , 17.0 , - 5.723585101952381 },
        { 2.0 , 18.0 , - 5.834810737062605 },
//        { 3.0 , 8.0 , - 6.579251212010101 },
//        { 3.0 , 9.0 , - 6.897704943128636 },
        { 3.0 , 10.0 , - 7.185387015580416 },
        { 3.0 , 11.0 , - 7.447751280047908 },
        { 3.0 , 12.0 , - 7.688913336864796 },
        { 3.0 , 13.0 , - 7.912056888179006 },
        { 3.0 , 14.0 , - 8.11969625295725 },
        { 3.0 , 15.0 , - 8.313852267398207 },
        { 3.0 , 16.0 , - 8.496173824192162 },
        { 3.0 , 17.0 , - 8.668024081118821 },
        { 3.0 , 18.0 , - 8.830543010616596 },
//        { 4.0 , 8.0 , - 8.977146484808472 },
//        { 4.0 , 9.0 , - 9.382611592916636 },
        { 4.0 , 10.0 , - 9.750336373041954 },
        { 4.0 , 11.0 , - 10.08680860966317 },
        { 4.0 , 12.0 , - 10.39696353796701 },
        { 4.0 , 13.0 , - 10.68464561041879 },
        { 4.0 , 14.0 , - 10.95290959701347 },
        { 4.0 , 15.0 , - 11.20422402529437 },
        { 4.0 , 16.0 , - 11.4406128033586 },
        { 4.0 , 17.0 , - 11.66375635467281 },
        { 4.0 , 18.0 , - 11.87506544834002 },
//        { 5.0 , 8.0 , - 11.46205313459647 },
//        { 5.0 , 9.0 , - 11.94756095037817 },
        { 5.0 , 10.0 , - 12.38939370265721 },
        { 5.0 , 11.0 , - 12.79485881076538 },
        { 5.0 , 12.0 , - 13.16955226020679 },
        { 5.0 , 13.0 , - 13.517858954475 },
        { 5.0 , 14.0 , - 13.84328135490963 },
        { 5.0 , 15.0 , - 14.14866300446081 },
        { 5.0 , 16.0 , - 14.43634507691259 },
        { 5.0 , 17.0 , - 14.70827879239624 },
        { 5.0 , 18.0 , - 14.96610790169833 },
//        { 6.0 , 8.0 , - 14.02700249205801 },
//        { 6.0 , 9.0 , - 14.58661827999343 },
        { 6.0 , 10.0 , - 15.09744390375942 },
        { 6.0 , 11.0 , - 15.56744753300516 },
        { 6.0 , 12.0 , - 16.002765604263 },
        { 6.0 , 13.0 , - 16.40823071237117 },
        { 6.0 , 14.0 , - 16.78772033407607 },
        { 6.0 , 15.0 , - 17.14439527801481 },
        { 6.0 , 16.0 , - 17.48086751463602 },
        { 6.0 , 17.0 , - 17.79932124575455 },
        { 6.0 , 18.0 , - 18.10160211762749 },
//        { 7.0 , 8.0 , - 16.66605982167327 },
//        { 7.0 , 9.0 , - 17.29466848109564 },
        { 7.0 , 10.0 , - 17.8700326259992 },
        { 7.0 , 11.0 , - 18.40066087706137 },
        { 7.0 , 12.0 , - 18.89313736215917 },
        { 7.0 , 13.0 , - 19.35266969153761 },
        { 7.0 , 14.0 , - 19.78345260763006 },
        { 7.0 , 15.0 , - 20.18891771573823 },
        { 7.0 , 16.0 , - 20.57190996799433 },
        { 7.0 , 17.0 , - 20.9348154616837 },
        { 7.0 , 18.0 , - 21.27965594797543 },
//        { 8.0 , 8.0 , - 19.37411002277548 },
//        { 8.0 , 9.0 , - 20.06725720333542 },
        { 8.0 , 10.0 , - 20.70324597005542 },
        { 8.0 , 11.0 , - 21.29103263495754 },
        { 8.0 , 12.0 , - 21.83757634132561 },
        { 8.0 , 13.0 , - 22.3484019650916 },
        { 8.0 , 14.0 , - 22.82797504535349 },
        { 8.0 , 15.0 , - 23.27996016909654 },
        { 8.0 , 16.0 , - 23.70740418392348 },
        { 8.0 , 17.0 , - 24.11286929203165 },
        { 8.0 , 18.0 , - 24.49853177284363 },
//        { 9.0 , 8.0 , - 22.14669874501526 },
//        { 9.0 , 9.0 , - 22.90047054739164 },
        { 9.0 , 10.0 , - 23.59361772795159 },
        { 9.0 , 11.0 , - 24.23547161412398 },
        { 9.0 , 12.0 , - 24.8333086148796 },
        { 9.0 , 13.0 , - 25.39292440281502 },
        { 9.0 , 14.0 , - 25.9190174987118 },
        { 9.0 , 15.0 , - 26.41545438502569 },
        { 9.0 , 16.0 , - 26.88545801427143 },
        { 9.0 , 17.0 , - 27.33174511689985 },
        { 9.0 , 18.0 , - 27.75662831086511 },
//        { 10.0 , 8.0 , - 24.97991208907148 },
//        { 10.0 , 9.0 , - 25.7908423052878 },
        { 10.0 , 10.0 , - 26.53805670711802 },
        { 10.0 , 11.0 , - 27.23120388767797 },
        { 10.0 , 12.0 , - 27.87783105260302 },
        { 10.0 , 13.0 , - 28.48396685617334 },
        { 10.0 , 14.0 , - 29.05451171464095 },
        { 10.0 , 15.0 , - 29.59350821537364 },
        { 10.0 , 16.0 , - 30.10433383913963 },
        { 10.0 , 17.0 , - 30.58984165492133 },
        { 10.0 , 18.0 , - 31.05246517686944 },
    };

    private static double logGammaMinusLogGammaSum(final double a, final double b) {

        /*
         * Use reflection to access private method.
         */
        try {
            final Method m = LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD;
            return ((Double) m.invoke(null, a, b)).doubleValue();
        } catch (final IllegalAccessException e) {
            Assert.fail(e.getMessage());
        } catch (final IllegalArgumentException e) {
            Assert.fail(e.getMessage());
        } catch (final InvocationTargetException e) {
            final Throwable te = e.getTargetException();
            if (te instanceof MathIllegalArgumentException) {
                throw (MathIllegalArgumentException) te;
            }
            Assert.fail(e.getMessage());
        }
        return Double.NaN;
    }

    @Test
    public void testLogGammaMinusLogGammaSum() {
        final int ulps = 4;
        for (int i = 0; i < LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF.length; i++) {
            final double[] ref = LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF[i];
            final double a = ref[0];
            final double b = ref[1];
            final double expected = ref[2];
            final double actual = logGammaMinusLogGammaSum(a, b);
            final double tol = ulps * FastMath.ulp(expected);
            final StringBuilder builder = new StringBuilder();
            builder.append(a).append(", ").append(b);
            Assert.assertEquals(builder.toString(), expected, actual, tol);
        }
    }

    @Test(expected = NumberIsTooSmallException.class)
    public void testLogGammaMinusLogGammaSumPrecondition1() {
        logGammaMinusLogGammaSum(-1.0, 8.0);
    }

    @Test(expected = NumberIsTooSmallException.class)
    public void testLogGammaMinusLogGammaSumPrecondition2() {
        logGammaMinusLogGammaSum(1.0, 7.0);
    }

    private static final double[][] SUM_DELTA_MINUS_DELTA_SUM_REF = {
        { 10.0 , 10.0 , .01249480717472882 },
        { 10.0 , 11.0 , .01193628470267385 },
        { 10.0 , 12.0 , .01148578547212797 },
        { 10.0 , 13.0 , .01111659739668398 },
        { 10.0 , 14.0 , .01080991216314295 },
        { 10.0 , 15.0 , .01055214134859758 },
        { 10.0 , 16.0 , .01033324912491747 },
        { 10.0 , 17.0 , .01014568069918883 },
        { 10.0 , 18.0 , .009983653199146491 },
        { 10.0 , 19.0 , .009842674320242729 },
        { 10.0 , 20.0 , 0.0097192081956071 },
        { 11.0 , 10.0 , .01193628470267385 },
        { 11.0 , 11.0 , .01135973290745925 },
        { 11.0 , 12.0 , .01089355537047828 },
        { 11.0 , 13.0 , .01051064829297728 },
        { 11.0 , 14.0 , 0.0101918899639826 },
        { 11.0 , 15.0 , .009923438811859604 },
        { 11.0 , 16.0 , .009695052724952705 },
        { 11.0 , 17.0 , 0.00949900745283617 },
        { 11.0 , 18.0 , .009329379874933402 },
        { 11.0 , 19.0 , 0.00918156080743147 },
        { 11.0 , 20.0 , 0.00905191635141762 },
        { 12.0 , 10.0 , .01148578547212797 },
        { 12.0 , 11.0 , .01089355537047828 },
        { 12.0 , 12.0 , .01041365883144029 },
        { 12.0 , 13.0 , .01001867865848564 },
        { 12.0 , 14.0 , 0.00968923999191334 },
        { 12.0 , 15.0 , .009411294976563555 },
        { 12.0 , 16.0 , .009174432043268762 },
        { 12.0 , 17.0 , .008970786693291802 },
        { 12.0 , 18.0 , .008794318926790865 },
        { 12.0 , 19.0 , .008640321527910711 },
        { 12.0 , 20.0 , .008505077879954796 },
        { 13.0 , 10.0 , .01111659739668398 },
        { 13.0 , 11.0 , .01051064829297728 },
        { 13.0 , 12.0 , .01001867865848564 },
        { 13.0 , 13.0 , .009613018147953376 },
        { 13.0 , 14.0 , .009274085618154277 },
        { 13.0 , 15.0 , 0.0089876637564166 },
        { 13.0 , 16.0 , .008743200745261382 },
        { 13.0 , 17.0 , .008532715206686251 },
        { 13.0 , 18.0 , .008350069108807093 },
        { 13.0 , 19.0 , .008190472517984874 },
        { 13.0 , 20.0 , .008050138630244345 },
        { 14.0 , 10.0 , .01080991216314295 },
        { 14.0 , 11.0 , 0.0101918899639826 },
        { 14.0 , 12.0 , 0.00968923999191334 },
        { 14.0 , 13.0 , .009274085618154277 },
        { 14.0 , 14.0 , .008926676241967286 },
        { 14.0 , 15.0 , .008632654302369184 },
        { 14.0 , 16.0 , .008381351102615795 },
        { 14.0 , 17.0 , .008164687232662443 },
        { 14.0 , 18.0 , .007976441942841219 },
        { 14.0 , 19.0 , .007811755112234388 },
        { 14.0 , 20.0 , .007666780069317652 },
        { 15.0 , 10.0 , .01055214134859758 },
        { 15.0 , 11.0 , .009923438811859604 },
        { 15.0 , 12.0 , .009411294976563555 },
        { 15.0 , 13.0 , 0.0089876637564166 },
        { 15.0 , 14.0 , .008632654302369184 },
        { 15.0 , 15.0 , 0.00833179217417291 },
        { 15.0 , 16.0 , .008074310643041299 },
        { 15.0 , 17.0 , .007852047581145882 },
        { 15.0 , 18.0 , .007658712051540045 },
        { 15.0 , 19.0 , .007489384065757007 },
        { 15.0 , 20.0 , .007340165635725612 },
        { 16.0 , 10.0 , .01033324912491747 },
        { 16.0 , 11.0 , .009695052724952705 },
        { 16.0 , 12.0 , .009174432043268762 },
        { 16.0 , 13.0 , .008743200745261382 },
        { 16.0 , 14.0 , .008381351102615795 },
        { 16.0 , 15.0 , .008074310643041299 },
        { 16.0 , 16.0 , .007811229919967624 },
        { 16.0 , 17.0 , .007583876618287594 },
        { 16.0 , 18.0 , .007385899933505551 },
        { 16.0 , 19.0 , .007212328560607852 },
        { 16.0 , 20.0 , .007059220321091879 },
        { 17.0 , 10.0 , .01014568069918883 },
        { 17.0 , 11.0 , 0.00949900745283617 },
        { 17.0 , 12.0 , .008970786693291802 },
        { 17.0 , 13.0 , .008532715206686251 },
        { 17.0 , 14.0 , .008164687232662443 },
        { 17.0 , 15.0 , .007852047581145882 },
        { 17.0 , 16.0 , .007583876618287594 },
        { 17.0 , 17.0 , .007351882161431358 },
        { 17.0 , 18.0 , .007149662089534654 },
        { 17.0 , 19.0 , .006972200907152378 },
        { 17.0 , 20.0 , .006815518216094137 },
        { 18.0 , 10.0 , .009983653199146491 },
        { 18.0 , 11.0 , .009329379874933402 },
        { 18.0 , 12.0 , .008794318926790865 },
        { 18.0 , 13.0 , .008350069108807093 },
        { 18.0 , 14.0 , .007976441942841219 },
        { 18.0 , 15.0 , .007658712051540045 },
        { 18.0 , 16.0 , .007385899933505551 },
        { 18.0 , 17.0 , .007149662089534654 },
        { 18.0 , 18.0 , .006943552208153373 },
        { 18.0 , 19.0 , .006762516574228829 },
        { 18.0 , 20.0 , .006602541598043117 },
        { 19.0 , 10.0 , .009842674320242729 },
        { 19.0 , 11.0 , 0.00918156080743147 },
        { 19.0 , 12.0 , .008640321527910711 },
        { 19.0 , 13.0 , .008190472517984874 },
        { 19.0 , 14.0 , .007811755112234388 },
        { 19.0 , 15.0 , .007489384065757007 },
        { 19.0 , 16.0 , .007212328560607852 },
        { 19.0 , 17.0 , .006972200907152378 },
        { 19.0 , 18.0 , .006762516574228829 },
        { 19.0 , 19.0 , .006578188655176814 },
        { 19.0 , 20.0 , .006415174623476747 },
        { 20.0 , 10.0 , 0.0097192081956071 },
        { 20.0 , 11.0 , 0.00905191635141762 },
        { 20.0 , 12.0 , .008505077879954796 },
        { 20.0 , 13.0 , .008050138630244345 },
        { 20.0 , 14.0 , .007666780069317652 },
        { 20.0 , 15.0 , .007340165635725612 },
        { 20.0 , 16.0 , .007059220321091879 },
        { 20.0 , 17.0 , .006815518216094137 },
        { 20.0 , 18.0 , .006602541598043117 },
        { 20.0 , 19.0 , .006415174623476747 },
        { 20.0 , 20.0 , .006249349445691423 },
    };

    private static double sumDeltaMinusDeltaSum(final double a,
                                                final double b) {

        /*
         * Use reflection to access private method.
         */
        try {
            final Method m = SUM_DELTA_MINUS_DELTA_SUM_METHOD;
            return ((Double) m.invoke(null, a, b)).doubleValue();
        } catch (final IllegalAccessException e) {
            Assert.fail(e.getMessage());
        } catch (final IllegalArgumentException e) {
            Assert.fail(e.getMessage());
        } catch (final InvocationTargetException e) {
            final Throwable te = e.getTargetException();
            if (te instanceof MathIllegalArgumentException) {
                throw (MathIllegalArgumentException) te;
            }
            Assert.fail(e.getMessage());
        }
        return Double.NaN;
    }

    @Test
    public void testSumDeltaMinusDeltaSum() {

        final int ulps = 3;
        for (int i = 0; i < SUM_DELTA_MINUS_DELTA_SUM_REF.length; i++) {
            final double[] ref = SUM_DELTA_MINUS_DELTA_SUM_REF[i];
            final double a = ref[0];
            final double b = ref[1];
            final double expected = ref[2];
            final double actual = sumDeltaMinusDeltaSum(a, b);
            final double tol = ulps * FastMath.ulp(expected);
            final StringBuilder builder = new StringBuilder();
            builder.append(a).append(", ").append(b);
            Assert.assertEquals(builder.toString(), expected, actual, tol);
        }
    }

    @Test(expected = NumberIsTooSmallException.class)
    public void testSumDeltaMinusDeltaSumPrecondition1() {

        sumDeltaMinusDeltaSum(9.0, 10.0);
    }

    @Test(expected = NumberIsTooSmallException.class)
    public void testSumDeltaMinusDeltaSumPrecondition2() {

        sumDeltaMinusDeltaSum(10.0, 9.0);
    }

    private static final double[][] LOG_BETA_REF = {
        { 0.125 , 0.125 , 2.750814190409515 },
        { 0.125 , 0.25 , 2.444366899981226 },
        { 0.125 , 0.5 , 2.230953804989556 },
        { 0.125 , 1.0 , 2.079441541679836 },
        { 0.125 , 2.0 , 1.961658506023452 },
        { 0.125 , 3.0 , 1.901033884207018 },
        { 0.125 , 4.0 , 1.860211889686763 },
        { 0.125 , 5.0 , 1.829440231020009 },
        { 0.125 , 6.0 , 1.804747618429637 },
        { 0.125 , 7.0 , 1.784128331226902 },
        { 0.125 , 8.0 , 1.766428754127501 },
        { 0.125 , 9.0 , 1.750924567591535 },
        { 0.125 , 10.0 , 1.7371312454592 },
        { 0.125 , 1000.0 , 1.156003642015969 },
        { 0.125 , 1001.0 , 1.155878649827818 },
        { 0.125 , 10000.0 , .8681312798751318 },
        { 0.25 , 0.125 , 2.444366899981226 },
        { 0.25 , 0.25 , 2.003680106471455 },
        { 0.25 , 0.5 , 1.657106516191482 },
        { 0.25 , 1.0 , 1.386294361119891 },
        { 0.25 , 2.0 , 1.163150809805681 },
        { 0.25 , 3.0 , 1.045367774149297 },
        { 0.25 , 4.0 , 0.965325066475761 },
        { 0.25 , 5.0 , .9047004446593261 },
        { 0.25 , 6.0 , .8559102804898941 },
        { 0.25 , 7.0 , 0.815088285969639 },
        { 0.25 , 8.0 , .7799969661583689 },
        { 0.25 , 9.0 , .7492253074916152 },
        { 0.25 , 10.0 , .7218263333035008 },
        { 0.25 , 1000.0 , - .4388225372378877 },
        { 0.25 , 1001.0 , - .4390725059930951 },
        { 0.25 , 10000.0 , - 1.014553193217846 },
        { 0.5 , 0.125 , 2.230953804989556 },
        { 0.5 , 0.25 , 1.657106516191482 },
        { 0.5 , 0.5 , 1.1447298858494 },
        { 0.5 , 1.0 , .6931471805599453 },
        { 0.5 , 2.0 , .2876820724517809 },
        { 0.5 , 3.0 , .06453852113757118 },
//        { 0.5 , 4.0 , - .08961215868968714 },
        { 0.5 , 5.0 , - .2073951943460706 },
        { 0.5 , 6.0 , - .3027053741503954 },
        { 0.5 , 7.0 , - .3827480818239319 },
        { 0.5 , 8.0 , - .4517409533108833 },
        { 0.5 , 9.0 , - .5123655751273182 },
        { 0.5 , 10.0 , - .5664327963975939 },
        { 0.5 , 1000.0 , - 2.881387696571577 },
        { 0.5 , 1001.0 , - 2.881887571613228 },
        { 0.5 , 10000.0 , - 4.032792743063396 },
        { 1.0 , 0.125 , 2.079441541679836 },
        { 1.0 , 0.25 , 1.386294361119891 },
        { 1.0 , 0.5 , .6931471805599453 },
        { 1.0 , 1.0 , 0.0 },
        { 1.0 , 2.0 , - .6931471805599453 },
        { 1.0 , 3.0 , - 1.09861228866811 },
        { 1.0 , 4.0 , - 1.386294361119891 },
        { 1.0 , 5.0 , - 1.6094379124341 },
        { 1.0 , 6.0 , - 1.791759469228055 },
        { 1.0 , 7.0 , - 1.945910149055313 },
        { 1.0 , 8.0 , - 2.079441541679836 },
        { 1.0 , 9.0 , - 2.19722457733622 },
        { 1.0 , 10.0 , - 2.302585092994046 },
        { 1.0 , 1000.0 , - 6.907755278982137 },
        { 1.0 , 1001.0 , - 6.90875477931522 },
        { 1.0 , 10000.0 , - 9.210340371976184 },
        { 2.0 , 0.125 , 1.961658506023452 },
        { 2.0 , 0.25 , 1.163150809805681 },
        { 2.0 , 0.5 , .2876820724517809 },
        { 2.0 , 1.0 , - .6931471805599453 },
        { 2.0 , 2.0 , - 1.791759469228055 },
        { 2.0 , 3.0 , - 2.484906649788 },
        { 2.0 , 4.0 , - 2.995732273553991 },
        { 2.0 , 5.0 , - 3.401197381662155 },
        { 2.0 , 6.0 , - 3.737669618283368 },
        { 2.0 , 7.0 , - 4.02535169073515 },
        { 2.0 , 8.0 , - 4.276666119016055 },
        { 2.0 , 9.0 , - 4.499809670330265 },
        { 2.0 , 10.0 , - 4.700480365792417 },
        { 2.0 , 1000.0 , - 13.81651005829736 },
        { 2.0 , 1001.0 , - 13.81850806096003 },
        { 2.0 , 10000.0 , - 18.4207807389527 },
        { 3.0 , 0.125 , 1.901033884207018 },
        { 3.0 , 0.25 , 1.045367774149297 },
        { 3.0 , 0.5 , .06453852113757118 },
        { 3.0 , 1.0 , - 1.09861228866811 },
        { 3.0 , 2.0 , - 2.484906649788 },
        { 3.0 , 3.0 , - 3.401197381662155 },
        { 3.0 , 4.0 , - 4.0943445622221 },
        { 3.0 , 5.0 , - 4.653960350157523 },
        { 3.0 , 6.0 , - 5.123963979403259 },
        { 3.0 , 7.0 , - 5.529429087511423 },
        { 3.0 , 8.0 , - 5.886104031450156 },
        { 3.0 , 9.0 , - 6.20455776256869 },
        { 3.0 , 10.0 , - 6.492239835020471 },
        { 3.0 , 1000.0 , - 20.03311615938222 },
        { 3.0 , 1001.0 , - 20.03611166836202 },
        { 3.0 , 10000.0 , - 26.9381739103716 },
        { 4.0 , 0.125 , 1.860211889686763 },
        { 4.0 , 0.25 , 0.965325066475761 },
//        { 4.0 , 0.5 , - .08961215868968714 },
        { 4.0 , 1.0 , - 1.386294361119891 },
        { 4.0 , 2.0 , - 2.995732273553991 },
        { 4.0 , 3.0 , - 4.0943445622221 },
        { 4.0 , 4.0 , - 4.941642422609304 },
        { 4.0 , 5.0 , - 5.634789603169249 },
        { 4.0 , 6.0 , - 6.222576268071369 },
        { 4.0 , 7.0 , - 6.733401891837359 },
        { 4.0 , 8.0 , - 7.185387015580416 },
        { 4.0 , 9.0 , - 7.590852123688581 },
        { 4.0 , 10.0 , - 7.958576903813898 },
        { 4.0 , 1000.0 , - 25.84525465867605 },
        { 4.0 , 1001.0 , - 25.84924667994559 },
        { 4.0 , 10000.0 , - 35.05020194868867 },
        { 5.0 , 0.125 , 1.829440231020009 },
        { 5.0 , 0.25 , .9047004446593261 },
        { 5.0 , 0.5 , - .2073951943460706 },
        { 5.0 , 1.0 , - 1.6094379124341 },
        { 5.0 , 2.0 , - 3.401197381662155 },
        { 5.0 , 3.0 , - 4.653960350157523 },
        { 5.0 , 4.0 , - 5.634789603169249 },
        { 5.0 , 5.0 , - 6.445719819385578 },
        { 5.0 , 6.0 , - 7.138866999945524 },
        { 5.0 , 7.0 , - 7.745002803515839 },
        { 5.0 , 8.0 , - 8.283999304248526 },
        { 5.0 , 9.0 , - 8.769507120030227 },
        { 5.0 , 10.0 , - 9.211339872309265 },
        { 5.0 , 1000.0 , - 31.37070759780783 },
        { 5.0 , 1001.0 , - 31.37569513931887 },
        { 5.0 , 10000.0 , - 42.87464787956629 },
        { 6.0 , 0.125 , 1.804747618429637 },
        { 6.0 , 0.25 , .8559102804898941 },
        { 6.0 , 0.5 , - .3027053741503954 },
        { 6.0 , 1.0 , - 1.791759469228055 },
        { 6.0 , 2.0 , - 3.737669618283368 },
        { 6.0 , 3.0 , - 5.123963979403259 },
        { 6.0 , 4.0 , - 6.222576268071369 },
        { 6.0 , 5.0 , - 7.138866999945524 },
        { 6.0 , 6.0 , - 7.927324360309794 },
        { 6.0 , 7.0 , - 8.620471540869739 },
        { 6.0 , 8.0 , - 9.239510749275963 },
        { 6.0 , 9.0 , - 9.799126537211386 },
        { 6.0 , 10.0 , - 10.30995216097738 },
        { 6.0 , 1000.0 , - 36.67401250586691 },
        { 6.0 , 1001.0 , - 36.67999457754446 },
        { 6.0 , 10000.0 , - 50.47605021415003 },
        { 7.0 , 0.125 , 1.784128331226902 },
        { 7.0 , 0.25 , 0.815088285969639 },
        { 7.0 , 0.5 , - .3827480818239319 },
        { 7.0 , 1.0 , - 1.945910149055313 },
        { 7.0 , 2.0 , - 4.02535169073515 },
        { 7.0 , 3.0 , - 5.529429087511423 },
        { 7.0 , 4.0 , - 6.733401891837359 },
        { 7.0 , 5.0 , - 7.745002803515839 },
        { 7.0 , 6.0 , - 8.620471540869739 },
        { 7.0 , 7.0 , - 9.39366142910322 },
        { 7.0 , 8.0 , - 10.08680860966317 },
        { 7.0 , 9.0 , - 10.71541726908554 },
        { 7.0 , 10.0 , - 11.2907814139891 },
        { 7.0 , 1000.0 , - 41.79599038729854 },
        { 7.0 , 1001.0 , - 41.80296600103496 },
        { 7.0 , 10000.0 , - 57.89523093697012 },
        { 8.0 , 0.125 , 1.766428754127501 },
        { 8.0 , 0.25 , .7799969661583689 },
        { 8.0 , 0.5 , - .4517409533108833 },
        { 8.0 , 1.0 , - 2.079441541679836 },
        { 8.0 , 2.0 , - 4.276666119016055 },
        { 8.0 , 3.0 , - 5.886104031450156 },
        { 8.0 , 4.0 , - 7.185387015580416 },
        { 8.0 , 5.0 , - 8.283999304248526 },
        { 8.0 , 6.0 , - 9.239510749275963 },
        { 8.0 , 7.0 , - 10.08680860966317 },
        { 8.0 , 8.0 , - 10.84894866171006 },
        { 8.0 , 9.0 , - 11.54209584227001 },
        { 8.0 , 10.0 , - 12.17808460899001 },
        { 8.0 , 1000.0 , - 46.76481113096179 },
        { 8.0 , 1001.0 , - 46.77277930061096 },
        { 8.0 , 10000.0 , - 65.16036091500527 },
        { 9.0 , 0.125 , 1.750924567591535 },
        { 9.0 , 0.25 , .7492253074916152 },
        { 9.0 , 0.5 , - .5123655751273182 },
        { 9.0 , 1.0 , - 2.19722457733622 },
        { 9.0 , 2.0 , - 4.499809670330265 },
        { 9.0 , 3.0 , - 6.20455776256869 },
        { 9.0 , 4.0 , - 7.590852123688581 },
        { 9.0 , 5.0 , - 8.769507120030227 },
        { 9.0 , 6.0 , - 9.799126537211386 },
        { 9.0 , 7.0 , - 10.71541726908554 },
        { 9.0 , 8.0 , - 11.54209584227001 },
        { 9.0 , 9.0 , - 12.29586764464639 },
        { 9.0 , 10.0 , - 12.98901482520633 },
        { 9.0 , 1000.0 , - 51.60109303791327 },
        { 9.0 , 1001.0 , - 51.61005277928474 },
        { 9.0 , 10000.0 , - 72.29205942547217 },
        { 10.0 , 0.125 , 1.7371312454592 },
        { 10.0 , 0.25 , .7218263333035008 },
        { 10.0 , 0.5 , - .5664327963975939 },
        { 10.0 , 1.0 , - 2.302585092994046 },
        { 10.0 , 2.0 , - 4.700480365792417 },
        { 10.0 , 3.0 , - 6.492239835020471 },
        { 10.0 , 4.0 , - 7.958576903813898 },
        { 10.0 , 5.0 , - 9.211339872309265 },
        { 10.0 , 6.0 , - 10.30995216097738 },
        { 10.0 , 7.0 , - 11.2907814139891 },
        { 10.0 , 8.0 , - 12.17808460899001 },
        { 10.0 , 9.0 , - 12.98901482520633 },
        { 10.0 , 10.0 , - 13.73622922703655 },
        { 10.0 , 1000.0 , - 56.32058348093065 },
        { 10.0 , 1001.0 , - 56.33053381178382 },
        { 10.0 , 10000.0 , - 79.30607481535498 },
        { 1000.0 , 0.125 , 1.156003642015969 },
        { 1000.0 , 0.25 , - .4388225372378877 },
        { 1000.0 , 0.5 , - 2.881387696571577 },
        { 1000.0 , 1.0 , - 6.907755278982137 },
        { 1000.0 , 2.0 , - 13.81651005829736 },
        { 1000.0 , 3.0 , - 20.03311615938222 },
        { 1000.0 , 4.0 , - 25.84525465867605 },
        { 1000.0 , 5.0 , - 31.37070759780783 },
        { 1000.0 , 6.0 , - 36.67401250586691 },
        { 1000.0 , 7.0 , - 41.79599038729854 },
        { 1000.0 , 8.0 , - 46.76481113096179 },
        { 1000.0 , 9.0 , - 51.60109303791327 },
        { 1000.0 , 10.0 , - 56.32058348093065 },
        { 1000.0 , 1000.0 , - 1388.482601635902 },
        { 1000.0 , 1001.0 , - 1389.175748816462 },
        { 1000.0 , 10000.0 , - 3353.484270767097 },
        { 1001.0 , 0.125 , 1.155878649827818 },
        { 1001.0 , 0.25 , - .4390725059930951 },
        { 1001.0 , 0.5 , - 2.881887571613228 },
        { 1001.0 , 1.0 , - 6.90875477931522 },
        { 1001.0 , 2.0 , - 13.81850806096003 },
        { 1001.0 , 3.0 , - 20.03611166836202 },
        { 1001.0 , 4.0 , - 25.84924667994559 },
        { 1001.0 , 5.0 , - 31.37569513931887 },
        { 1001.0 , 6.0 , - 36.67999457754446 },
        { 1001.0 , 7.0 , - 41.80296600103496 },
        { 1001.0 , 8.0 , - 46.77277930061096 },
        { 1001.0 , 9.0 , - 51.61005277928474 },
        { 1001.0 , 10.0 , - 56.33053381178382 },
        { 1001.0 , 1000.0 , - 1389.175748816462 },
        { 1001.0 , 1001.0 , - 1389.869395872064 },
        { 1001.0 , 10000.0 , - 3355.882166039895 },
        { 10000.0 , 0.125 , .8681312798751318 },
        { 10000.0 , 0.25 , - 1.014553193217846 },
        { 10000.0 , 0.5 , - 4.032792743063396 },
        { 10000.0 , 1.0 , - 9.210340371976184 },
        { 10000.0 , 2.0 , - 18.4207807389527 },
        { 10000.0 , 3.0 , - 26.9381739103716 },
        { 10000.0 , 4.0 , - 35.05020194868867 },
        { 10000.0 , 5.0 , - 42.87464787956629 },
        { 10000.0 , 6.0 , - 50.47605021415003 },
        { 10000.0 , 7.0 , - 57.89523093697012 },
        { 10000.0 , 8.0 , - 65.16036091500527 },
        { 10000.0 , 9.0 , - 72.29205942547217 },
        { 10000.0 , 10.0 , - 79.30607481535498 },
        { 10000.0 , 1000.0 , - 3353.484270767097 },
        { 10000.0 , 1001.0 , - 3355.882166039895 },
        { 10000.0 , 10000.0 , - 13866.28325676141 },
    };

    @Test
    public void testLogBeta() {
        final int ulps = 3;
        for (int i = 0; i < LOG_BETA_REF.length; i++) {
            final double[] ref = LOG_BETA_REF[i];
            final double a = ref[0];
            final double b = ref[1];
            final double expected = ref[2];
            final double actual = Beta.logBeta(a, b);
            final double tol = ulps * FastMath.ulp(expected);
            final StringBuilder builder = new StringBuilder();
            builder.append(a).append(", ").append(b);
            Assert.assertEquals(builder.toString(), expected, actual, tol);
        }
    }}

Other Java examples (source code examples)

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my book on functional programming

 

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