MATH-849: new unit test showing the relative accuracy of
Gamma.logGamma(double). git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1374909 13f79535-47bb-0310-9956-ffa450edef68
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Sebastien Brisard
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74d366c819
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@ -150,6 +150,134 @@ public class GammaTest {
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}
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}
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/**
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* Reference data for the {@link Gamma#logGamma(double)} function. This data
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* was generated with the following <a
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* href="http://maxima.sourceforge.net/">Maxima</a> script.
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*
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* <pre>
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* kill(all);
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*
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* fpprec : 64;
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* gamln(x) := log(gamma(x));
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* x : append(makelist(bfloat(i / 8), i, 1, 80),
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* [0.8b0, 1b2, 1b3, 1b4, 1b5, 1b6, 1b7, 1b8, 1b9, 1b10]);
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*
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* for i : 1 while i <= length(x) do
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* print("{", float(x[i]), ",", float(gamln(x[i])), "},");
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* </pre>
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*/
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private static final double[][] LOG_GAMMA_REF = {
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{ 0.125 , 2.019418357553796 },
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{ 0.25 , 1.288022524698077 },
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{ 0.375 , .8630739822706475 },
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{ 0.5 , .5723649429247001 },
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{ 0.625 , .3608294954889402 },
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{ 0.75 , .2032809514312954 },
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{ 0.875 , .08585870722533433 },
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{ 1.0 , 0.0 },
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{ 1.125 , - .06002318412603958 },
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{ 1.25 , - .09827183642181316 },
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{ 1.375 , - .1177552707410788 },
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{ 1.5 , - .1207822376352452 },
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{ 1.625 , - .1091741337567954 },
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{ 1.75 , - .08440112102048555 },
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{ 1.875 , - 0.0476726853991883 },
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{ 2.0 , 0.0 },
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{ 2.125 , .05775985153034387 },
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{ 2.25 , .1248717148923966 },
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{ 2.375 , .2006984603774558 },
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{ 2.5 , .2846828704729192 },
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{ 2.625 , .3763336820249054 },
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{ 2.75 , .4752146669149371 },
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{ 2.875 , .5809359740231859 },
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{ 3.0 , .6931471805599453 },
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{ 3.125 , 0.811531653906724 },
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{ 3.25 , .9358019311087253 },
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{ 3.375 , 1.06569589786406 },
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{ 3.5 , 1.200973602347074 },
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{ 3.625 , 1.341414578068493 },
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{ 3.75 , 1.486815578593417 },
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{ 3.875 , 1.6369886482725 },
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{ 4.0 , 1.791759469228055 },
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{ 4.125 , 1.950965937095089 },
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{ 4.25 , 2.114456927450371 },
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{ 4.375 , 2.282091222188554 },
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{ 4.5 , 2.453736570842442 },
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{ 4.625 , 2.62926886637513 },
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{ 4.75 , 2.808571418575736 },
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{ 4.875 , 2.99153431107781 },
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{ 5.0 , 3.178053830347946 },
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{ 5.125 , 3.368031956881733 },
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{ 5.25 , 3.561375910386697 },
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{ 5.375 , 3.757997741998131 },
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{ 5.5 , 3.957813967618717 },
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{ 5.625 , 4.160745237339519 },
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{ 5.75 , 4.366716036622286 },
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{ 5.875 , 4.57565441552762 },
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{ 6.0 , 4.787491742782046 },
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{ 6.125 , 5.002162481906205 },
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{ 6.25 , 5.219603986990229 },
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{ 6.375 , 5.439756316011858 },
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{ 6.5 , 5.662562059857142 },
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{ 6.625 , 5.887966185430003 },
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{ 6.75 , 6.115915891431546 },
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{ 6.875 , 6.346360475557843 },
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{ 7.0 , 6.579251212010101 },
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{ 7.125 , 6.814541238336996 },
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{ 7.25 , 7.05218545073854 },
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{ 7.375 , 7.292140407056348 },
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{ 7.5 , 7.534364236758733 },
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{ 7.625 , 7.778816557302289 },
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{ 7.75 , 8.025458396315983 },
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{ 7.875 , 8.274252119110479 },
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{ 8.0 , 8.525161361065415 },
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{ 8.125 , 8.77815096449171 },
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{ 8.25 , 9.033186919605123 },
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{ 8.375 , 9.290236309282232 },
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{ 8.5 , 9.549267257300997 },
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{ 8.625 , 9.810248879795765 },
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{ 8.75 , 10.07315123968124 },
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{ 8.875 , 10.33794530382217 },
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{ 9.0 , 10.60460290274525 },
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{ 9.125 , 10.87309669270751 },
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{ 9.25 , 11.14340011995171 },
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{ 9.375 , 11.41548738699336 },
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{ 9.5 , 11.68933342079727 },
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{ 9.625 , 11.96491384271319 },
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{ 9.75 , 12.24220494005076 },
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{ 9.875 , 12.52118363918365 },
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{ 10.0 , 12.80182748008147 },
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{ 0.8 , .1520596783998376 },
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{ 100.0 , 359.1342053695754 },
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{ 1000.0 , 5905.220423209181 },
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{ 10000.0 , 82099.71749644238 },
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{ 100000.0 , 1051287.708973657 },
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{ 1000000.0 , 1.2815504569147612e+7 },
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{ 10000000.0 , 1.511809493694739e+8 },
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{ 1.e+8 , 1.7420680661038346e+9 },
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{ 1.e+9 , 1.972326582750371e+10 },
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{ 1.e+10 , 2.202585092888106e+11 },
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};
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@Test
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public void testLogGamma() {
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final int ulps = 130;
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for (int i = 0; i < LOG_GAMMA_REF.length; i++) {
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final double[] data = LOG_GAMMA_REF[i];
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final double x = data[0];
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final double expected = data[1];
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final double actual = Gamma.logGamma(x);
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final double tol;
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if (expected == 0.0) {
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tol = 1E-15;
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} else {
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tol = ulps * FastMath.ulp(expected);
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}
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Assert.assertEquals(Double.toString(x), expected, actual, tol);
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}
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}
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private void checkRelativeError(String msg, double expected, double actual, double tolerance) {
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Assert.assertEquals(msg, expected, actual, FastMath.abs(tolerance * actual));
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}
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