http://git-wip-us.apache.org/repos/asf/commons-math/blob/44ab2569/src/test/java/org/apache/commons/math4/special/BetaTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math4/special/BetaTest.java b/src/test/java/org/apache/commons/math4/special/BetaTest.java deleted file mode 100644 index 5a42dbc..0000000 --- a/src/test/java/org/apache/commons/math4/special/BetaTest.java +++ /dev/null @@ -1,979 +0,0 @@ -/* - * 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.math4.special; - -import java.lang.reflect.InvocationTargetException; -import java.lang.reflect.Method; - -import org.apache.commons.math4.TestUtils; -import org.apache.commons.math4.exception.MathIllegalArgumentException; -import org.apache.commons.math4.exception.NumberIsTooSmallException; -import org.apache.commons.math4.exception.OutOfRangeException; -import org.apache.commons.math4.special.Beta; -import org.apache.commons.math4.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</a> 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); - } - }}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/44ab2569/src/test/java/org/apache/commons/math4/special/GammaTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/commons/math4/special/GammaTest.java b/src/test/java/org/apache/commons/math4/special/GammaTest.java deleted file mode 100644 index c320526..0000000 --- a/src/test/java/org/apache/commons/math4/special/GammaTest.java +++ /dev/null @@ -1,998 +0,0 @@ -/* - * 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.math4.special; - -import org.apache.commons.math4.TestUtils; -import org.apache.commons.math4.exception.NumberIsTooLargeException; -import org.apache.commons.math4.exception.NumberIsTooSmallException; -import org.apache.commons.math4.util.FastMath; -import org.junit.Assert; -import org.junit.Test; - -/** - */ -public class GammaTest { - private void testRegularizedGamma(double expected, double a, double x) { - double actualP = Gamma.regularizedGammaP(a, x); - double actualQ = Gamma.regularizedGammaQ(a, x); - TestUtils.assertEquals(expected, actualP, 10e-15); - TestUtils.assertEquals(actualP, 1.0 - actualQ, 10e-15); - } - - private void testLogGamma(double expected, double x) { - double actual = Gamma.logGamma(x); - TestUtils.assertEquals(expected, actual, 10e-15); - } - - @Test - public void testRegularizedGammaNanPositive() { - testRegularizedGamma(Double.NaN, Double.NaN, 1.0); - } - - @Test - public void testRegularizedGammaPositiveNan() { - testRegularizedGamma(Double.NaN, 1.0, Double.NaN); - } - - @Test - public void testRegularizedGammaNegativePositive() { - testRegularizedGamma(Double.NaN, -1.5, 1.0); - } - - @Test - public void testRegularizedGammaPositiveNegative() { - testRegularizedGamma(Double.NaN, 1.0, -1.0); - } - - @Test - public void testRegularizedGammaZeroPositive() { - testRegularizedGamma(Double.NaN, 0.0, 1.0); - } - - @Test - public void testRegularizedGammaPositiveZero() { - testRegularizedGamma(0.0, 1.0, 0.0); - } - - @Test - public void testRegularizedGammaPositivePositive() { - testRegularizedGamma(0.632120558828558, 1.0, 1.0); - } - - @Test - public void testLogGammaNan() { - testLogGamma(Double.NaN, Double.NaN); - } - - @Test - public void testLogGammaNegative() { - testLogGamma(Double.NaN, -1.0); - } - - @Test - public void testLogGammaZero() { - testLogGamma(Double.NaN, 0.0); - } - - @Test - public void testLogGammaPositive() { - testLogGamma(0.6931471805599457, 3.0); - } - - @Test - public void testDigammaLargeArgs() { - double eps = 1e-8; - Assert.assertEquals(4.6001618527380874002, Gamma.digamma(100), eps); - Assert.assertEquals(3.9019896734278921970, Gamma.digamma(50), eps); - Assert.assertEquals(2.9705239922421490509, Gamma.digamma(20), eps); - Assert.assertEquals(2.9958363947076465821, Gamma.digamma(20.5), eps); - Assert.assertEquals(2.2622143570941481605, Gamma.digamma(10.1), eps); - Assert.assertEquals(2.1168588189004379233, Gamma.digamma(8.8), eps); - Assert.assertEquals(1.8727843350984671394, Gamma.digamma(7), eps); - Assert.assertEquals(0.42278433509846713939, Gamma.digamma(2), eps); - Assert.assertEquals(-100.56088545786867450, Gamma.digamma(0.01), eps); - Assert.assertEquals(-4.0390398965921882955, Gamma.digamma(-0.8), eps); - Assert.assertEquals(4.2003210041401844726, Gamma.digamma(-6.3), eps); - Assert.assertEquals(-3.110625123035E-5, Gamma.digamma(1.4616), eps); - } - - @Test - public void testDigammaSmallArgs() { - // values for negative powers of 10 from 1 to 30 as computed by webMathematica with 20 digits - // see functions.wolfram.com - double[] expected = {-10.423754940411076795, -100.56088545786867450, -1000.5755719318103005, - -10000.577051183514335, -100000.57719921568107, -1.0000005772140199687e6, -1.0000000577215500408e7, - -1.0000000057721564845e8, -1.0000000005772156633e9, -1.0000000000577215665e10, -1.0000000000057721566e11, - -1.0000000000005772157e12, -1.0000000000000577216e13, -1.0000000000000057722e14, -1.0000000000000005772e15, -1e+16, - -1e+17, -1e+18, -1e+19, -1e+20, -1e+21, -1e+22, -1e+23, -1e+24, -1e+25, -1e+26, - -1e+27, -1e+28, -1e+29, -1e+30}; - for (double n = 1; n < 30; n++) { - checkRelativeError(String.format("Test %.0f: ", n), expected[(int) (n - 1)], Gamma.digamma(FastMath.pow(10.0, -n)), 1e-8); - } - } - - @Test - public void testDigammaNonRealArgs() { - Assert.assertTrue(Double.isNaN(Gamma.digamma(Double.NaN))); - Assert.assertTrue(Double.isInfinite(Gamma.digamma(Double.POSITIVE_INFINITY))); - Assert.assertTrue(Double.isInfinite(Gamma.digamma(Double.NEGATIVE_INFINITY))); - } - - @Test - public void testTrigamma() { - double eps = 1e-8; - // computed using webMathematica. For example, to compute trigamma($i) = Polygamma(1, $i), use - // - // http://functions.wolfram.com/webMathematica/Evaluated.jsp?name=PolyGamma2&plottype=0&vars={%221%22,%22$i%22}&digits=20 - double[] data = { - 1e-4, 1.0000000164469368793e8, - 1e-3, 1.0000016425331958690e6, - 1e-2, 10001.621213528313220, - 1e-1, 101.43329915079275882, - 1, 1.6449340668482264365, - 2, 0.64493406684822643647, - 3, 0.39493406684822643647, - 4, 0.28382295573711532536, - 5, 0.22132295573711532536, - 10, 0.10516633568168574612, - 20, 0.051270822935203119832, - 50, 0.020201333226697125806, - 100, 0.010050166663333571395 - }; - for (int i = data.length - 2; i >= 0; i -= 2) { - Assert.assertEquals(String.format("trigamma %.0f", data[i]), data[i + 1], Gamma.trigamma(data[i]), eps); - } - } - - @Test - public void testTrigammaNonRealArgs() { - Assert.assertTrue(Double.isNaN(Gamma.trigamma(Double.NaN))); - Assert.assertTrue(Double.isInfinite(Gamma.trigamma(Double.POSITIVE_INFINITY))); - Assert.assertTrue(Double.isInfinite(Gamma.trigamma(Double.NEGATIVE_INFINITY))); - } - - /** - * Reference data for the {@link Gamma#logGamma(double)} function. This data - * was generated with the following <a - * href="http://maxima.sourceforge.net/">Maxima</a> script. - * - * <pre> - * kill(all); - * - * fpprec : 64; - * gamln(x) := log(gamma(x)); - * x : append(makelist(bfloat(i / 8), i, 1, 80), - * [0.8b0, 1b2, 1b3, 1b4, 1b5, 1b6, 1b7, 1b8, 1b9, 1b10]); - * - * for i : 1 while i <= length(x) do - * print("{", float(x[i]), ",", float(gamln(x[i])), "},"); - * </pre> - */ - private static final double[][] LOG_GAMMA_REF = { - { 0.125 , 2.019418357553796 }, - { 0.25 , 1.288022524698077 }, - { 0.375 , .8630739822706475 }, - { 0.5 , .5723649429247001 }, - { 0.625 , .3608294954889402 }, - { 0.75 , .2032809514312954 }, - { 0.875 , .08585870722533433 }, - { 0.890625 , .07353860936979656 }, - { 0.90625 , .06169536624059108 }, - { 0.921875 , .05031670080005688 }, - { 0.9375 , 0.0393909017345823 }, - { 0.953125 , .02890678734595923 }, - { 0.96875 , .01885367233441289 }, - { 0.984375 , .009221337197578781 }, - { 1.0 , 0.0 }, - { 1.015625 , - 0.00881970970573307 }, - { 1.03125 , - .01724677500176807 }, - { 1.046875 , - .02528981394675729 }, - { 1.0625 , - .03295710029357782 }, - { 1.078125 , - .04025658272400143 }, - { 1.09375 , - .04719590272716985 }, - { 1.109375 , - .05378241123619192 }, - { 1.125 , - .06002318412603958 }, - { 1.25 , - .09827183642181316 }, - { 1.375 , - .1177552707410788 }, - { 1.5 , - .1207822376352452 }, - { 1.625 , - .1091741337567954 }, - { 1.75 , - .08440112102048555 }, - { 1.875 , - 0.0476726853991883 }, - { 1.890625 , - .04229320615532515 }, - { 1.90625 , - .03674470657266143 }, - { 1.921875 , - .03102893865389552 }, - { 1.9375 , - .02514761940298887 }, - { 1.953125 , - .01910243184040138 }, - { 1.96875 , - .01289502598016741 }, - { 1.984375 , - .006527019770560387 }, - { 2.0 , 0.0 }, - { 2.015625 , .006684476830232185 }, - { 2.03125 , .01352488366498562 }, - { 2.046875 , .02051972208453692 }, - { 2.0625 , .02766752152285702 }, - { 2.078125 , 0.0349668385135861 }, - { 2.09375 , .04241625596251728 }, - { 2.109375 , .05001438244545164 }, - { 2.125 , .05775985153034387 }, - { 2.25 , .1248717148923966 }, - { 2.375 , .2006984603774558 }, - { 2.5 , .2846828704729192 }, - { 2.625 , .3763336820249054 }, - { 2.75 , .4752146669149371 }, - { 2.875 , .5809359740231859 }, - { 2.890625 , .5946142560817441 }, - { 2.90625 , .6083932548009232 }, - { 2.921875 , .6222723333588501 }, - { 2.9375 , .6362508628423761 }, - { 2.953125 , .6503282221022278 }, - { 2.96875 , .6645037976116387 }, - { 2.984375 , 0.678776983328359 }, - { 3.0 , .6931471805599453 }, - { 3.015625 , .7076137978322324 }, - { 3.03125 , .7221762507608962 }, - { 3.046875 , .7368339619260166 }, - { 3.0625 , 0.751586360749556 }, - { 3.078125 , .7664328833756681 }, - { 3.09375 , .7813729725537568 }, - { 3.109375 , .7964060775242092 }, - { 3.125 , 0.811531653906724 }, - { 3.25 , .9358019311087253 }, - { 3.375 , 1.06569589786406 }, - { 3.5 , 1.200973602347074 }, - { 3.625 , 1.341414578068493 }, - { 3.75 , 1.486815578593417 }, - { 3.875 , 1.6369886482725 }, - { 4.0 , 1.791759469228055 }, - { 4.125 , 1.950965937095089 }, - { 4.25 , 2.114456927450371 }, - { 4.375 , 2.282091222188554 }, - { 4.5 , 2.453736570842442 }, - { 4.625 , 2.62926886637513 }, - { 4.75 , 2.808571418575736 }, - { 4.875 , 2.99153431107781 }, - { 5.0 , 3.178053830347946 }, - { 5.125 , 3.368031956881733 }, - { 5.25 , 3.561375910386697 }, - { 5.375 , 3.757997741998131 }, - { 5.5 , 3.957813967618717 }, - { 5.625 , 4.160745237339519 }, - { 5.75 , 4.366716036622286 }, - { 5.875 , 4.57565441552762 }, - { 6.0 , 4.787491742782046 }, - { 6.125 , 5.002162481906205 }, - { 6.25 , 5.219603986990229 }, - { 6.375 , 5.439756316011858 }, - { 6.5 , 5.662562059857142 }, - { 6.625 , 5.887966185430003 }, - { 6.75 , 6.115915891431546 }, - { 6.875 , 6.346360475557843 }, - { 7.0 , 6.579251212010101 }, - { 7.125 , 6.814541238336996 }, - { 7.25 , 7.05218545073854 }, - { 7.375 , 7.292140407056348 }, - { 7.5 , 7.534364236758733 }, - { 7.625 , 7.778816557302289 }, - { 7.75 , 8.025458396315983 }, - { 7.875 , 8.274252119110479 }, - { 8.0 , 8.525161361065415 }, - { 8.125 , 8.77815096449171 }, - { 8.25 , 9.033186919605123 }, - { 8.375 , 9.290236309282232 }, - { 8.5 , 9.549267257300997 }, - { 8.625 , 9.810248879795765 }, - { 8.75 , 10.07315123968124 }, - { 8.875 , 10.33794530382217 }, - { 9.0 , 10.60460290274525 }, - { 9.125 , 10.87309669270751 }, - { 9.25 , 11.14340011995171 }, - { 9.375 , 11.41548738699336 }, - { 9.5 , 11.68933342079727 }, - { 9.625 , 11.96491384271319 }, - { 9.75 , 12.24220494005076 }, - { 9.875 , 12.52118363918365 }, - { 10.0 , 12.80182748008147 }, - { 0.8 , .1520596783998376 }, - { 100.0 , 359.1342053695754 }, - { 1000.0 , 5905.220423209181 }, - { 10000.0 , 82099.71749644238 }, - { 100000.0 , 1051287.708973657 }, - { 1000000.0 , 1.2815504569147612e+7 }, - { 10000000.0 , 1.511809493694739e+8 }, - { 1.e+8 , 1.7420680661038346e+9 }, - { 1.e+9 , 1.972326582750371e+10 }, - { 1.e+10 , 2.202585092888106e+11 }, - }; - - @Test - public void testLogGamma() { - final int ulps = 3; - for (int i = 0; i < LOG_GAMMA_REF.length; i++) { - final double[] data = LOG_GAMMA_REF[i]; - final double x = data[0]; - final double expected = data[1]; - final double actual = Gamma.logGamma(x); - final double tol; - if (expected == 0.0) { - tol = 1E-15; - } else { - tol = ulps * FastMath.ulp(expected); - } - Assert.assertEquals(Double.toString(x), expected, actual, tol); - } - } - - @Test - public void testLogGammaPrecondition1() { - Assert.assertTrue(Double.isNaN(Gamma.logGamma(0.0))); - } - - @Test - public void testLogGammaPrecondition2() { - Assert.assertTrue(Double.isNaN(Gamma.logGamma(-1.0))); - } - - /** - * <p> - * Reference values for the {@link Gamma#invGamma1pm1(double)} method. - * These values were generated with the following <a - * href="http://maxima.sourceforge.net/">Maxima</a> script - * </p> - * - * <pre> - * kill(all); - * - * fpprec : 64; - * gam1(x) := 1 / gamma(1 + x) - 1; - * x : makelist(bfloat(i / 8), i, -4, 12); - * - * for i : 1 while i <= length(x) do print("{", - * float(x[i]), - * ",", - * float(gam1(x[i])), - * "},"); - * </pre> - */ - private static final double[][] INV_GAMMA1P_M1_REF = { - { -0.5 , -.4358104164522437 }, - { -0.375 , -.3029021533379859 }, - { -0.25 , -0.183951060901737 }, - { -0.125 , -.08227611018520711 }, - { 0.0 , 0.0 }, - { 0.125 , .06186116458306091 }, - { 0.25 , .1032626513208373 }, - { 0.375 , .1249687649039041 }, - { 0.5 , .1283791670955126 }, - { 0.625 , .1153565546592225 }, - { 0.75 , 0.0880652521310173 }, - { 0.875 , .04882730264547758 }, - { 1.0 , 0.0 }, - { 1.125 , -.05612340925950141 }, - { 1.25 , -.1173898789433302 }, - { 1.375 , -.1818408982517061 }, - { 1.5 , -0.247747221936325 }, - }; - - @Test - public void testInvGamma1pm1() { - - final int ulps = 3; - for (int i = 0; i < INV_GAMMA1P_M1_REF.length; i++) { - final double[] ref = INV_GAMMA1P_M1_REF[i]; - final double x = ref[0]; - final double expected = ref[1]; - final double actual = Gamma.invGamma1pm1(x); - final double tol = ulps * FastMath.ulp(expected); - Assert.assertEquals(Double.toString(x), expected, actual, tol); - } - } - - @Test(expected = NumberIsTooSmallException.class) - public void testInvGamma1pm1Precondition1() { - - Gamma.invGamma1pm1(-0.51); - } - - @Test(expected = NumberIsTooLargeException.class) - public void testInvGamma1pm1Precondition2() { - - Gamma.invGamma1pm1(1.51); - } - - private static final double[][] LOG_GAMMA1P_REF = { - { - 0.5 , .5723649429247001 }, - { - 0.375 , .3608294954889402 }, - { - 0.25 , .2032809514312954 }, - { - 0.125 , .08585870722533433 }, - { 0.0 , 0.0 }, - { 0.125 , - .06002318412603958 }, - { 0.25 , - .09827183642181316 }, - { 0.375 , - .1177552707410788 }, - { 0.5 , - .1207822376352452 }, - { 0.625 , - .1091741337567954 }, - { 0.75 , - .08440112102048555 }, - { 0.875 , - 0.0476726853991883 }, - { 1.0 , 0.0 }, - { 1.125 , .05775985153034387 }, - { 1.25 , .1248717148923966 }, - { 1.375 , .2006984603774558 }, - { 1.5 , .2846828704729192 }, - }; - - @Test - public void testLogGamma1p() { - - final int ulps = 3; - for (int i = 0; i < LOG_GAMMA1P_REF.length; i++) { - final double[] ref = LOG_GAMMA1P_REF[i]; - final double x = ref[0]; - final double expected = ref[1]; - final double actual = Gamma.logGamma1p(x); - final double tol = ulps * FastMath.ulp(expected); - Assert.assertEquals(Double.toString(x), expected, actual, tol); - } - } - - @Test(expected = NumberIsTooSmallException.class) - public void testLogGamma1pPrecondition1() { - - Gamma.logGamma1p(-0.51); - } - - @Test(expected = NumberIsTooLargeException.class) - public void testLogGamma1pPrecondition2() { - - Gamma.logGamma1p(1.51); - } - - /** - * Reference data for the {@link Gamma#gamma(double)} function. This - * data was generated with the following <a - * href="http://maxima.sourceforge.net/">Maxima</a> script. - * - * <pre> - * kill(all); - * - * fpprec : 64; - * - * EPSILON : 10**(-fpprec + 1); - * isInteger(x) := abs(x - floor(x)) <= EPSILON * abs(x); - * - * x : makelist(bfloat(i / 8), i, -160, 160); - * x : append(x, makelist(bfloat(i / 2), i, 41, 200)); - * - * for i : 1 while i <= length(x) do if not(isInteger(x[i])) then - * print("{", float(x[i]), ",", float(gamma(x[i])), "},"); - * </pre> - */ - private static final double[][] GAMMA_REF = { - { - 19.875 , 4.920331854832504e-18 }, - { - 19.75 , 3.879938752480031e-18 }, - { - 19.625 , 4.323498423815027e-18 }, - { - 19.5 , 5.811045977502237e-18 }, - { - 19.375 , 9.14330910942125e-18 }, - { - 19.25 , 1.735229114436739e-17 }, - { - 19.125 , 4.653521565668223e-17 }, - { - 18.875 , - 9.779159561479603e-17 }, - { - 18.75 , - 7.662879036148061e-17 }, - { - 18.625 , - 8.484865656736991e-17 }, - { - 18.5 , - 1.133153965612936e-16 }, - { - 18.375 , - 1.771516139950367e-16 }, - { - 18.25 , - 3.340316045290721e-16 }, - { - 18.125 , - 8.899859994340475e-16 }, - { - 17.875 , 1.845816367229275e-15 }, - { - 17.75 , 1.436789819277761e-15 }, - { - 17.625 , 1.580306228567265e-15 }, - { - 17.5 , 2.096334836383932e-15 }, - { - 17.375 , 3.255160907158799e-15 }, - { - 17.25 , 6.096076782655566e-15 }, - { - 17.125 , 1.613099623974211e-14 }, - { - 16.875 , - 3.29939675642233e-14 }, - { - 16.75 , - 2.550301929218027e-14 }, - { - 16.625 , - 2.785289727849803e-14 }, - { - 16.5 , - 3.66858596367188e-14 }, - { - 16.375 , - 5.655842076188414e-14 }, - { - 16.25 , - 1.051573245008085e-13 }, - { - 16.125 , - 2.762433106055837e-13 }, - { - 15.875 , 5.567732026462681e-13 }, - { - 15.75 , 4.271755731440195e-13 }, - { - 15.625 , 4.630544172550298e-13 }, - { - 15.5 , 6.053166840058604e-13 }, - { - 15.375 , 9.261441399758529e-13 }, - { - 15.25 , 1.708806523138138e-12 }, - { - 15.125 , 4.454423383515037e-12 }, - { - 14.875 , - 8.838774592009505e-12 }, - { - 14.75 , - 6.728015277018307e-12 }, - { - 14.625 , - 7.235225269609841e-12 }, - { - 14.5 , - 9.382408602090835e-12 }, - { - 14.375 , - 1.423946615212874e-11 }, - { - 14.25 , - 2.605929947785661e-11 }, - { - 14.125 , - 6.737315367566492e-11 }, - { - 13.875 , 1.314767720561414e-10 }, - { - 13.75 , 9.923822533602004e-11 }, - { - 13.625 , 1.058151695680439e-10 }, - { - 13.5 , 1.360449247303171e-10 }, - { - 13.375 , 2.046923259368506e-10 }, - { - 13.25 , 3.713450175594567e-10 }, - { - 13.125 , 9.516457956687671e-10 }, - { - 12.875 , - 1.8242402122789617e-9 }, - { - 12.75 , - 1.3645255983702756e-9 }, - { - 12.625 , - 1.4417316853645984e-9 }, - { - 12.5 , - 1.836606483859281e-9 }, - { - 12.375 , - 2.7377598594053765e-9 }, - { - 12.25 , - 4.9203214826628017e-9 }, - { - 12.125 , - 1.2490351068152569e-8 }, - { - 11.875 , 2.3487092733091633e-8 }, - { - 11.75 , 1.7397701379221012e-8 }, - { - 11.625 , 1.8201862527728055e-8 }, - { - 11.5 , 2.295758104824101e-8 }, - { - 11.375 , 3.3879778260141535e-8 }, - { - 11.25 , 6.027393816261931e-8 }, - { - 11.125 , 1.5144550670134987e-7 }, - { - 10.875 , - 2.7890922620546316e-7 }, - { - 10.75 , - 2.044229912058469e-7 }, - { - 10.625 , - 2.1159665188483867e-7 }, - { - 10.5 , - 2.640121820547716e-7 }, - { - 10.375 , - 3.8538247770911e-7 }, - { - 10.25 , - 6.780818043294673e-7 }, - { - 10.125 , - 1.6848312620525174e-6 }, - { - 9.875 , 3.0331378349844124e-6 }, - { - 9.75 , 2.1975471554628537e-6 }, - { - 9.625 , 2.2482144262764103e-6 }, - { - 9.5 , 2.772127911575102e-6 }, - { - 9.375 , 3.998343206232017e-6 }, - { - 9.25 , 6.95033849437704e-6 }, - { - 9.125 , 1.7058916528281737e-5 }, - { - 8.875 , - 2.9952236120471065e-5 }, - { - 8.75 , - 2.1426084765762826e-5 }, - { - 8.625 , - 2.163906385291045e-5 }, - { - 8.5 , - 2.633521515996347e-5 }, - { - 8.375 , - 3.748446755842515e-5 }, - { - 8.25 , - 6.429063107298763e-5 }, - { - 8.125 , - 1.5566261332057085e-4 }, - { - 7.875 , 2.658260955691807e-4 }, - { - 7.75 , 1.874782417004247e-4 }, - { - 7.625 , 1.8663692573135265e-4 }, - { - 7.5 , 2.238493288596895e-4 }, - { - 7.375 , 3.1393241580181064e-4 }, - { - 7.25 , 5.303977063521479e-4 }, - { - 7.125 , .001264758733229638 }, - { - 6.875 , - .002093380502607298 }, - { - 6.75 , - .001452956373178292 }, - { - 6.625 , - .001423106558701564 }, - { - 6.5 , - .001678869966447671 }, - { - 6.375 , - .002315251566538353 }, - { - 6.25 , - .003845383371053072 }, - { - 6.125 , - .009011405974261174 }, - { - 5.875 , .01439199095542518 }, - { - 5.75 , .009807455518953468 }, - { - 5.625 , .009428080951397862 }, - { - 5.5 , .01091265478190986 }, - { - 5.375 , 0.014759728736682 }, - { - 5.25 , 0.0240336460690817 }, - { - 5.125 , .05519486159234969 }, - { - 4.875 , - 0.0845529468631229 }, - { - 4.75 , - .05639286923398244 }, - { - 4.625 , - .05303295535161297 }, - { - 4.5 , - .06001960130050425 }, - { - 4.375 , - .07933354195966577 }, - { - 4.25 , - .1261766418626789 }, - { - 4.125 , - .2828736656607921 }, - { - 3.875 , .4121956159577241 }, - { - 3.75 , .2678661288614166 }, - { - 3.625 , 0.24527741850121 }, - { - 3.5 , .2700882058522691 }, - { - 3.375 , .3470842460735378 }, - { - 3.25 , .5362507279163854 }, - { - 3.125 , 1.166853870850768 }, - { - 2.875 , - 1.597258011836181 }, - { - 2.75 , - 1.004497983230312 }, - { - 2.625 , - .8891306420668862 }, - { - 2.5 , - .9453087204829419 }, - { - 2.375 , - 1.17140933049819 }, - { - 2.25 , - 1.742814865728253 }, - { - 2.125 , - 3.646418346408649 }, - { - 1.875 , 4.59211678402902 }, - { - 1.75 , 2.762369453883359 }, - { - 1.625 , 2.333967935425576 }, - { - 1.5 , 2.363271801207355 }, - { - 1.375 , 2.782097159933201 }, - { - 1.25 , 3.921333447888569 }, - { - 1.125 , 7.748638986118379 }, - { - 0.875 , - 8.610218970054413 }, - { - 0.75 , - 4.834146544295877 }, - { - 0.625 , - 3.792697895066561 }, - { - 0.5 , - 3.544907701811032 }, - { - 0.375 , - 3.825383594908152 }, - { - 0.25 , - 4.901666809860711 }, - { - 0.125 , - 8.717218859383175 }, - { 0.125 , 7.533941598797612 }, - { 0.25 , 3.625609908221908 }, - { 0.375 , 2.370436184416601 }, - { 0.5 , 1.772453850905516 }, - { 0.625 , 1.434518848090557 }, - { 0.75 , 1.225416702465178 }, - { 0.875 , 1.089652357422897 }, - { 1.0 , 1.0 }, - { 1.125 , .9417426998497015 }, - { 1.25 , 0.906402477055477 }, - { 1.375 , .8889135691562253 }, - { 1.5 , 0.886226925452758 }, - { 1.625 , 0.896574280056598 }, - { 1.75 , .9190625268488832 }, - { 1.875 , .9534458127450348 }, - { 2.0 , 1.0 }, - { 2.125 , 1.059460537330914 }, - { 2.25 , 1.133003096319346 }, - { 2.375 , 1.22225615758981 }, - { 2.5 , 1.329340388179137 }, - { 2.625 , 1.456933205091972 }, - { 2.75 , 1.608359421985546 }, - { 2.875 , 1.78771089889694 }, - { 3.0 , 2.0 }, - { 3.125 , 2.251353641828193 }, - { 3.25 , 2.549256966718529 }, - { 3.375 , 2.902858374275799 }, - { 3.5 , 3.323350970447843 }, - { 3.625 , 3.824449663366426 }, - { 3.75 , 4.422988410460251 }, - { 3.875 , 5.139668834328703 }, - { 4.0 , 6.0 }, - { 4.125 , 7.035480130713102 }, - { 4.25 , 8.28508514183522 }, - { 4.375 , 9.797147013180819 }, - { 4.5 , 11.63172839656745 }, - { 4.625 , 13.86363002970329 }, - { 4.75 , 16.58620653922594 }, - { 4.875 , 19.91621673302373 }, - { 5.0 , 24.0 }, - { 5.125 , 29.02135553919155 }, - { 5.25 , 35.21161185279968 }, - { 5.375 , 42.86251818266609 }, - { 5.5 , 52.34277778455352 }, - { 5.625 , 64.11928888737773 }, - { 5.75 , 78.78448106132322 }, - { 5.875 , 97.09155657349066 }, - { 6.0 , 120.0 }, - { 6.125 , 148.7344471383567 }, - { 6.25 , 184.8609622271983 }, - { 6.375 , 230.3860352318302 }, - { 6.5 , 287.8852778150443 }, - { 6.625 , 360.6709999914997 }, - { 6.75 , 453.0107661026085 }, - { 6.875 , 570.4128948692577 }, - { 7.0 , 720.0 }, - { 7.125 , 910.9984887224346 }, - { 7.25 , 1155.38101391999 }, - { 7.375 , 1468.710974602918 }, - { 7.5 , 1871.254305797788 }, - { 7.625 , 2389.445374943686 }, - { 7.75 , 3057.822671192607 }, - { 7.875 , 3921.588652226146 }, - { 8.0 , 5040.0 }, - { 8.125 , 6490.864232147346 }, - { 8.25 , 8376.512350919926 }, - { 8.375 , 10831.74343769652 }, - { 8.5 , 14034.40729348341 }, - { 8.625 , 18219.5209839456 }, - { 8.75 , 23698.12570174271 }, - { 8.875 , 30882.5106362809 }, - { 9.0 , 40320.0 }, - { 9.125 , 52738.27188619719 }, - { 9.25 , 69106.22689508938 }, - { 9.375 , 90715.85129070834 }, - { 9.5 , 119292.461994609 }, - { 9.625 , 157143.3684865308 }, - { 9.75 , 207358.5998902487 }, - { 9.875 , 274082.281896993 }, - { 10.0 , 362880.0 }, - { 10.125 , 481236.7309615494 }, - { 10.25 , 639232.5987795768 }, - { 10.375 , 850461.1058503906 }, - { 10.5 , 1133278.388948786 }, - { 10.625 , 1512504.921682859 }, - { 10.75 , 2021746.348929925 }, - { 10.875 , 2706562.533732806 }, - { 11.0 , 3628800.0 }, - { 11.125 , 4872521.900985687 }, - { 11.25 , 6552134.137490662 }, - { 11.375 , 8823533.973197803 }, - { 11.5 , 1.1899423083962249e+7 }, - { 11.625 , 1.6070364792880382e+7 }, - { 11.75 , 2.1733773250996688e+7 }, - { 11.875 , 2.943386755434427e+7 }, - { 12.0 , 3.99168e+7 }, - { 12.125 , 5.420680614846578e+7 }, - { 12.25 , 7.371150904676994e+7 }, - { 12.375 , 1.0036769894512501e+8 }, - { 12.5 , 1.3684336546556586e+8 }, - { 12.625 , 1.8681799071723443e+8 }, - { 12.75 , 2.5537183569921107e+8 }, - { 12.875 , 3.4952717720783816e+8 }, - { 13.0 , 4.790016e+8 }, - { 13.125 , 6.572575245501475e+8 }, - { 13.25 , 9.029659858229319e+8 }, - { 13.375 , 1.2420502744459219e+9 }, - { 13.5 , 1.7105420683195732e+9 }, - { 13.625 , 2.3585771328050845e+9 }, - { 13.75 , 3.2559909051649416e+9 }, - { 13.875 , 4.500162406550916e+9 }, - { 14.0 , 6.2270208e+9 }, - { 14.125 , 8.626505009720685e+9 }, - { 14.25 , 1.196429931215385e+10 }, - { 14.375 , 1.66124224207142e+10 }, - { 14.5 , 2.309231792231424e+10 }, - { 14.625 , 3.213561343446927e+10 }, - { 14.75 , 4.476987494601794e+10 }, - { 14.875 , 6.243975339089396e+10 }, - { 15.0 , 8.71782912e+10 }, - { 15.125 , 1.218493832623047e+11 }, - { 15.25 , 1.704912651981923e+11 }, - { 15.375 , 2.388035722977667e+11 }, - { 15.5 , 3.348386098735565e+11 }, - { 15.625 , 4.699833464791132e+11 }, - { 15.75 , 6.603556554537646e+11 }, - { 15.875 , 9.287913316895475e+11 }, - { 16.0 , 1.307674368e+12 }, - { 16.125 , 1.842971921842358e+12 }, - { 16.25 , 2.599991794272433e+12 }, - { 16.375 , 3.671604924078163e+12 }, - { 16.5 , 5.189998453040126e+12 }, - { 16.625 , 7.343489788736144e+12 }, - { 16.75 , 1.040060157339679e+13 }, - { 16.875 , 1.474456239057157e+13 }, - { 17.0 , 2.0922789888e+13 }, - { 17.125 , 2.971792223970803e+13 }, - { 17.25 , 4.224986665692704e+13 }, - { 17.375 , 6.012253063177992e+13 }, - { 17.5 , 8.563497447516206e+13 }, - { 17.625 , 1.220855177377384e+14 }, - { 17.75 , 1.742100763543963e+14 }, - { 17.875 , 2.488144903408952e+14 }, - { 18.0 , 3.55687428096e+14 }, - { 18.125 , 5.08919418355e+14 }, - { 18.25 , 7.288101998319914e+14 }, - { 18.375 , 1.044628969727176e+15 }, - { 18.5 , 1.498612053315336e+15 }, - { 18.625 , 2.151757250127639e+15 }, - { 18.75 , 3.092228855290534e+15 }, - { 18.875 , 4.447559014843502e+15 }, - { 19.0 , 6.402373705728e+15 }, - { 19.125 , 9.224164457684374e+15 }, - { 19.25 , 1.330078614693384e+16 }, - { 19.375 , 1.919505731873686e+16 }, - { 19.5 , 2.772432298633372e+16 }, - { 19.625 , 4.007647878362728e+16 }, - { 19.75 , 5.797929103669752e+16 }, - { 19.875 , 8.39476764051711e+16 }, - { 20.0 , 1.21645100408832e+17 }, - { 20.5 , 5.406242982335075e+17 }, - { 21.0 , 2.43290200817664e+18 }, - { 21.5 , 1.10827981137869e+19 }, - { 22.0 , 5.109094217170944e+19 }, - { 22.5 , 2.382801594464184e+20 }, - { 23.0 , 1.124000727777608e+21 }, - { 23.5 , 5.361303587544415e+21 }, - { 24.0 , 2.585201673888498e+22 }, - { 24.5 , 1.259906343072938e+23 }, - { 25.0 , 6.204484017332395e+23 }, - { 25.5 , 3.086770540528697e+24 }, - { 26.0 , 1.551121004333099e+25 }, - { 26.5 , 7.871264878348176e+25 }, - { 27.0 , 4.032914611266056e+26 }, - { 27.5 , 2.085885192762267e+27 }, - { 28.0 , 1.088886945041835e+28 }, - { 28.5 , 5.736184280096234e+28 }, - { 29.0 , 3.048883446117139e+29 }, - { 29.5 , 1.634812519827427e+30 }, - { 30.0 , 8.841761993739702e+30 }, - { 30.5 , 4.822696933490909e+31 }, - { 31.0 , 2.65252859812191e+32 }, - { 31.5 , 1.470922564714727e+33 }, - { 32.0 , 8.222838654177922e+33 }, - { 32.5 , 4.633406078851391e+34 }, - { 33.0 , 2.631308369336935e+35 }, - { 33.5 , 1.505856975626702e+36 }, - { 34.0 , 8.683317618811885e+36 }, - { 34.5 , 5.044620868349451e+37 }, - { 35.0 , 2.952327990396041e+38 }, - { 35.5 , 1.740394199580561e+39 }, - { 36.0 , 1.033314796638614e+40 }, - { 36.5 , 6.178399408510991e+40 }, - { 37.0 , 3.719933267899013e+41 }, - { 37.5 , 2.255115784106512e+42 }, - { 38.0 , 1.376375309122634e+43 }, - { 38.5 , 8.456684190399419e+43 }, - { 39.0 , 5.230226174666011e+44 }, - { 39.5 , 3.255823413303776e+45 }, - { 40.0 , 2.039788208119745e+46 }, - { 40.5 , 1.286050248254992e+47 }, - { 41.0 , 8.159152832478976e+47 }, - { 41.5 , 5.208503505432716e+48 }, - { 42.0 , 3.345252661316381e+49 }, - { 42.5 , 2.161528954754577e+50 }, - { 43.0 , 1.40500611775288e+51 }, - { 43.5 , 9.186498057706953e+51 }, - { 44.0 , 6.041526306337383e+52 }, - { 44.5 , 3.996126655102524e+53 }, - { 45.0 , 2.658271574788449e+54 }, - { 45.5 , 1.778276361520623e+55 }, - { 46.0 , 1.196222208654802e+56 }, - { 46.5 , 8.091157444918836e+56 }, - { 47.0 , 5.502622159812088e+57 }, - { 47.5 , 3.762388211887259e+58 }, - { 48.0 , 2.586232415111682e+59 }, - { 48.5 , 1.787134400646448e+60 }, - { 49.0 , 1.241391559253607e+61 }, - { 49.5 , 8.667601843135273e+61 }, - { 50.0 , 6.082818640342675e+62 }, - { 50.5 , 4.290462912351959e+63 }, - { 51.0 , 3.041409320171338e+64 }, - { 51.5 , 2.16668377073774e+65 }, - { 52.0 , 1.551118753287382e+66 }, - { 52.5 , 1.115842141929936e+67 }, - { 53.0 , 8.065817517094388e+67 }, - { 53.5 , 5.858171245132164e+68 }, - { 54.0 , 4.274883284060025e+69 }, - { 54.5 , 3.134121616145708e+70 }, - { 55.0 , 2.308436973392413e+71 }, - { 55.5 , 1.70809628079941e+72 }, - { 56.0 , 1.269640335365828e+73 }, - { 56.5 , 9.479934358436728e+73 }, - { 57.0 , 7.109985878048635e+74 }, - { 57.5 , 5.356162912516752e+75 }, - { 58.0 , 4.052691950487721e+76 }, - { 58.5 , 3.079793674697132e+77 }, - { 59.0 , 2.350561331282878e+78 }, - { 59.5 , 1.801679299697822e+79 }, - { 60.0 , 1.386831185456898e+80 }, - { 60.5 , 1.071999183320204e+81 }, - { 61.0 , 8.320987112741391e+81 }, - { 61.5 , 6.485595059087236e+82 }, - { 62.0 , 5.075802138772249e+83 }, - { 62.5 , 3.98864096133865e+84 }, - { 63.0 , 3.146997326038794e+85 }, - { 63.5 , 2.492900600836656e+86 }, - { 64.0 , 1.98260831540444e+87 }, - { 64.5 , 1.582991881531277e+88 }, - { 65.0 , 1.268869321858841e+89 }, - { 65.5 , 1.021029763587673e+90 }, - { 66.0 , 8.247650592082472e+90 }, - { 66.5 , 6.687744951499262e+91 }, - { 67.0 , 5.443449390774431e+92 }, - { 67.5 , 4.447350392747009e+93 }, - { 68.0 , 3.647111091818868e+94 }, - { 68.5 , 3.001961515104231e+95 }, - { 69.0 , 2.48003554243683e+96 }, - { 69.5 , 2.056343637846398e+97 }, - { 70.0 , 1.711224524281413e+98 }, - { 70.5 , 1.429158828303247e+99 }, - { 71.0 , 1.19785716699699e+100 }, - { 71.5 , 1.00755697395379e+101 }, - { 72.0 , 8.50478588567862e+101 }, - { 72.5 , 7.20403236376959e+102 }, - { 73.0 , 6.12344583768861e+103 }, - { 73.5 , 5.22292346373295e+104 }, - { 74.0 , 4.47011546151268e+105 }, - { 74.5 , 3.83884874584372e+106 }, - { 75.0 , 3.30788544151939e+107 }, - { 75.5 , 2.85994231565357e+108 }, - { 76.0 , 2.48091408113954e+109 }, - { 76.5 , 2.15925644831845e+110 }, - { 77.0 , 1.88549470166605e+111 }, - { 77.5 , 1.65183118296361e+112 }, - { 78.0 , 1.45183092028286e+113 }, - { 78.5 , 1.2801691667968e+114 }, - { 79.0 , 1.13242811782063e+115 }, - { 79.5 , 1.00493279593549e+116 }, - { 80.0 , 8.94618213078298e+116 }, - { 80.5 , 7.98921572768712e+117 }, - { 81.0 , 7.15694570462638e+118 }, - { 81.5 , 6.43131866078814e+119 }, - { 82.0 , 5.79712602074737e+120 }, - { 82.5 , 5.24152470854233e+121 }, - { 83.0 , 4.75364333701284e+122 }, - { 83.5 , 4.32425788454742e+123 }, - { 84.0 , 3.94552396972066e+124 }, - { 84.5 , 3.6107553335971e+125 }, - { 85.0 , 3.31424013456535e+126 }, - { 85.5 , 3.05108825688955e+127 }, - { 86.0 , 2.81710411438055e+128 }, - { 86.5 , 2.60868045964056e+129 }, - { 87.0 , 2.42270953836727e+130 }, - { 87.5 , 2.25650859758909e+131 }, - { 88.0 , 2.10775729837953e+132 }, - { 88.5 , 1.97444502289045e+133 }, - { 89.0 , 1.85482642257398e+134 }, - { 89.5 , 1.74738384525805e+135 }, - { 90.0 , 1.65079551609085e+136 }, - { 90.5 , 1.56390854150595e+137 }, - { 91.0 , 1.48571596448176e+138 }, - { 91.5 , 1.41533723006289e+139 }, - { 92.0 , 1.3520015276784e+140 }, - { 92.5 , 1.29503356550754e+141 }, - { 93.0 , 1.24384140546413e+142 }, - { 93.5 , 1.19790604809448e+143 }, - { 94.0 , 1.15677250708164e+144 }, - { 94.5 , 1.12004215496834e+145 }, - { 95.0 , 1.08736615665674e+146 }, - { 95.5 , 1.05843983644508e+147 }, - { 96.0 , 1.03299784882391e+148 }, - { 96.5 , 1.01081004380505e+149 }, - { 97.0 , 9.9167793487095e+149 }, - { 97.5 , 9.75431692271873e+150 }, - { 98.0 , 9.61927596824821e+151 }, - { 98.5 , 9.51045899965076e+152 }, - { 99.0 , 9.42689044888325e+153 }, - { 99.5 , 9.367802114656e+154 }, - { 100.0 , 9.33262154439441e+155 }, - }; - - @Test - public void testGamma() { - - for (int i = 0; i < GAMMA_REF.length; i++) { - final double[] ref = GAMMA_REF[i]; - final double x = ref[0]; - final double expected = ref[1]; - final double actual = Gamma.gamma(x); - final double absX = FastMath.abs(x); - final int ulps; - if (absX <= 8.0) { - ulps = 3; - } else if (absX <= 20.0) { - ulps = 5; - } else if (absX <= 30.0) { - ulps = 50; - } else if (absX <= 50.0) { - ulps = 180; - } else { - ulps = 500; - } - final double tol = ulps * FastMath.ulp(expected); - Assert.assertEquals(Double.toString(x), expected, actual, tol); - } - } - - @Test - public void testGammaNegativeInteger() { - - for (int i = -100; i <= 0; i++) { - Assert.assertTrue(Integer.toString(i), Double.isNaN(Gamma.gamma(i))); - } - } - - @Test - public void testGammaNegativeDouble() { - // check that the gamma function properly switches sign - // see: https://en.wikipedia.org/wiki/Gamma_function - - double previousGamma = Gamma.gamma(-18.5); - for (double x = -19.5; x > -25; x -= 1.0) { - double gamma = Gamma.gamma(x); - Assert.assertEquals( (int) FastMath.signum(previousGamma), - - (int) FastMath.signum(gamma)); - - previousGamma = gamma; - } - } - - private void checkRelativeError(String msg, double expected, double actual, - double tolerance) { - - Assert.assertEquals(msg, expected, actual, FastMath.abs(tolerance * actual)); - } -}