| /* |
| * 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 org.apache.commons.math3.TestUtils; |
| import org.apache.commons.math3.exception.NumberIsTooLargeException; |
| import org.apache.commons.math3.exception.NumberIsTooSmallException; |
| import org.apache.commons.math3.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); |
| } |
| |
| @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 }, |
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| { 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)); |
| } |
| } |
