| /* |
| * 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.distribution; |
| |
| import java.io.BufferedReader; |
| import java.io.IOException; |
| import java.io.InputStream; |
| import java.io.InputStreamReader; |
| |
| import org.apache.commons.math3.exception.NotStrictlyPositiveException; |
| import org.apache.commons.math3.special.Gamma; |
| import org.apache.commons.math3.stat.descriptive.SummaryStatistics; |
| import org.apache.commons.math3.util.FastMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| /** |
| * Test cases for GammaDistribution. |
| * Extends ContinuousDistributionAbstractTest. See class javadoc for |
| * ContinuousDistributionAbstractTest for details. |
| * |
| */ |
| public class GammaDistributionTest extends RealDistributionAbstractTest { |
| |
| //-------------- Implementations for abstract methods ----------------------- |
| |
| /** Creates the default continuous distribution instance to use in tests. */ |
| @Override |
| public GammaDistribution makeDistribution() { |
| return new GammaDistribution(4d, 2d); |
| } |
| |
| /** Creates the default cumulative probability distribution test input values */ |
| @Override |
| public double[] makeCumulativeTestPoints() { |
| // quantiles computed using R version 2.9.2 |
| return new double[] {0.857104827257, 1.64649737269, 2.17973074725, 2.7326367935, 3.48953912565, |
| 26.1244815584, 20.0902350297, 17.5345461395, 15.5073130559, 13.3615661365}; |
| } |
| |
| /** Creates the default cumulative probability density test expected values */ |
| @Override |
| public double[] makeCumulativeTestValues() { |
| return new double[] {0.001, 0.01, 0.025, 0.05, 0.1, 0.999, 0.990, 0.975, 0.950, 0.900}; |
| } |
| |
| /** Creates the default probability density test expected values */ |
| @Override |
| public double[] makeDensityTestValues() { |
| return new double[] {0.00427280075546, 0.0204117166709, 0.0362756163658, 0.0542113174239, 0.0773195272491, |
| 0.000394468852816, 0.00366559696761, 0.00874649473311, 0.0166712508128, 0.0311798227954}; |
| } |
| |
| // --------------------- Override tolerance -------------- |
| @Override |
| public void setUp() { |
| super.setUp(); |
| setTolerance(1e-9); |
| } |
| |
| //---------------------------- Additional test cases ------------------------- |
| @SuppressWarnings("deprecation") |
| @Test |
| public void testParameterAccessors() { |
| GammaDistribution distribution = (GammaDistribution) getDistribution(); |
| Assert.assertEquals(4d, distribution.getAlpha(), 0); |
| Assert.assertEquals(2d, distribution.getBeta(), 0); |
| } |
| |
| @Test |
| public void testPreconditions() { |
| try { |
| new GammaDistribution(0, 1); |
| Assert.fail("Expecting NotStrictlyPositiveException for alpha = 0"); |
| } catch (NotStrictlyPositiveException ex) { |
| // Expected. |
| } |
| try { |
| new GammaDistribution(1, 0); |
| Assert.fail("Expecting NotStrictlyPositiveException for alpha = 0"); |
| } catch (NotStrictlyPositiveException ex) { |
| // Expected. |
| } |
| } |
| |
| @Test |
| public void testProbabilities() { |
| testProbability(-1.000, 4.0, 2.0, .0000); |
| testProbability(15.501, 4.0, 2.0, .9499); |
| testProbability(0.504, 4.0, 1.0, .0018); |
| testProbability(10.011, 1.0, 2.0, .9933); |
| testProbability(5.000, 2.0, 2.0, .7127); |
| } |
| |
| @Test |
| public void testValues() { |
| testValue(15.501, 4.0, 2.0, .9499); |
| testValue(0.504, 4.0, 1.0, .0018); |
| testValue(10.011, 1.0, 2.0, .9933); |
| testValue(5.000, 2.0, 2.0, .7127); |
| } |
| |
| private void testProbability(double x, double a, double b, double expected) { |
| GammaDistribution distribution = new GammaDistribution( a, b ); |
| double actual = distribution.cumulativeProbability(x); |
| Assert.assertEquals("probability for " + x, expected, actual, 10e-4); |
| } |
| |
| private void testValue(double expected, double a, double b, double p) { |
| GammaDistribution distribution = new GammaDistribution( a, b ); |
| double actual = distribution.inverseCumulativeProbability(p); |
| Assert.assertEquals("critical value for " + p, expected, actual, 10e-4); |
| } |
| |
| @Test |
| public void testDensity() { |
| double[] x = new double[]{-0.1, 1e-6, 0.5, 1, 2, 5}; |
| // R2.5: print(dgamma(x, shape=1, rate=1), digits=10) |
| checkDensity(1, 1, x, new double[]{0.000000000000, 0.999999000001, 0.606530659713, 0.367879441171, 0.135335283237, 0.006737946999}); |
| // R2.5: print(dgamma(x, shape=2, rate=1), digits=10) |
| checkDensity(2, 1, x, new double[]{0.000000000000, 0.000000999999, 0.303265329856, 0.367879441171, 0.270670566473, 0.033689734995}); |
| // R2.5: print(dgamma(x, shape=4, rate=1), digits=10) |
| checkDensity(4, 1, x, new double[]{0.000000000e+00, 1.666665000e-19, 1.263605541e-02, 6.131324020e-02, 1.804470443e-01, 1.403738958e-01}); |
| // R2.5: print(dgamma(x, shape=4, rate=10), digits=10) |
| checkDensity(4, 10, x, new double[]{0.000000000e+00, 1.666650000e-15, 1.403738958e+00, 7.566654960e-02, 2.748204830e-05, 4.018228850e-17}); |
| // R2.5: print(dgamma(x, shape=.1, rate=10), digits=10) |
| checkDensity(0.1, 10, x, new double[]{0.000000000e+00, 3.323953832e+04, 1.663849010e-03, 6.007786726e-06, 1.461647647e-10, 5.996008322e-24}); |
| // R2.5: print(dgamma(x, shape=.1, rate=20), digits=10) |
| checkDensity(0.1, 20, x, new double[]{0.000000000e+00, 3.562489883e+04, 1.201557345e-05, 2.923295295e-10, 3.228910843e-19, 1.239484589e-45}); |
| // R2.5: print(dgamma(x, shape=.1, rate=4), digits=10) |
| checkDensity(0.1, 4, x, new double[]{0.000000000e+00, 3.032938388e+04, 3.049322494e-02, 2.211502311e-03, 2.170613371e-05, 5.846590589e-11}); |
| // R2.5: print(dgamma(x, shape=.1, rate=1), digits=10) |
| checkDensity(0.1, 1, x, new double[]{0.000000000e+00, 2.640334143e+04, 1.189704437e-01, 3.866916944e-02, 7.623306235e-03, 1.663849010e-04}); |
| } |
| |
| private void checkDensity(double alpha, double rate, double[] x, double[] expected) { |
| GammaDistribution d = new GammaDistribution(alpha, 1 / rate); |
| for (int i = 0; i < x.length; i++) { |
| Assert.assertEquals(expected[i], d.density(x[i]), 1e-5); |
| } |
| } |
| |
| @Test |
| public void testInverseCumulativeProbabilityExtremes() { |
| setInverseCumulativeTestPoints(new double[] {0, 1}); |
| setInverseCumulativeTestValues(new double[] {0, Double.POSITIVE_INFINITY}); |
| verifyInverseCumulativeProbabilities(); |
| } |
| |
| @Test |
| public void testMoments() { |
| final double tol = 1e-9; |
| GammaDistribution dist; |
| |
| dist = new GammaDistribution(1, 2); |
| Assert.assertEquals(dist.getNumericalMean(), 2, tol); |
| Assert.assertEquals(dist.getNumericalVariance(), 4, tol); |
| |
| dist = new GammaDistribution(1.1, 4.2); |
| Assert.assertEquals(dist.getNumericalMean(), 1.1d * 4.2d, tol); |
| Assert.assertEquals(dist.getNumericalVariance(), 1.1d * 4.2d * 4.2d, tol); |
| } |
| |
| private static final double HALF_LOG_2_PI = 0.5 * FastMath.log(2.0 * FastMath.PI); |
| |
| public static double logGamma(double x) { |
| /* |
| * This is a copy of |
| * double Gamma.logGamma(double) |
| * prior to MATH-849 |
| */ |
| double ret; |
| |
| if (Double.isNaN(x) || (x <= 0.0)) { |
| ret = Double.NaN; |
| } else { |
| double sum = Gamma.lanczos(x); |
| double tmp = x + Gamma.LANCZOS_G + .5; |
| ret = ((x + .5) * FastMath.log(tmp)) - tmp + |
| HALF_LOG_2_PI + FastMath.log(sum / x); |
| } |
| |
| return ret; |
| } |
| |
| public static double density(final double x, final double shape, |
| final double scale) { |
| /* |
| * This is a copy of |
| * double GammaDistribution.density(double) |
| * prior to MATH-753. |
| */ |
| if (x < 0) { |
| return 0; |
| } |
| return FastMath.pow(x / scale, shape - 1) / scale * |
| FastMath.exp(-x / scale) / FastMath.exp(logGamma(shape)); |
| } |
| |
| /* |
| * MATH-753: large values of x or shape parameter cause density(double) to |
| * overflow. Reference data is generated with the Maxima script |
| * gamma-distribution.mac, which can be found in |
| * src/test/resources/org/apache/commons/math3/distribution. |
| */ |
| |
| private void doTestMath753(final double shape, |
| final double meanNoOF, final double sdNoOF, |
| final double meanOF, final double sdOF, |
| final String resourceName) throws IOException { |
| final GammaDistribution distribution = new GammaDistribution(shape, 1.0); |
| final SummaryStatistics statOld = new SummaryStatistics(); |
| final SummaryStatistics statNewNoOF = new SummaryStatistics(); |
| final SummaryStatistics statNewOF = new SummaryStatistics(); |
| |
| final InputStream resourceAsStream; |
| resourceAsStream = this.getClass().getResourceAsStream(resourceName); |
| Assert.assertNotNull("Could not find resource " + resourceName, |
| resourceAsStream); |
| final BufferedReader in; |
| in = new BufferedReader(new InputStreamReader(resourceAsStream)); |
| |
| try { |
| for (String line = in.readLine(); line != null; line = in.readLine()) { |
| if (line.startsWith("#")) { |
| continue; |
| } |
| final String[] tokens = line.split(", "); |
| Assert.assertTrue("expected two floating-point values", |
| tokens.length == 2); |
| final double x = Double.parseDouble(tokens[0]); |
| final String msg = "x = " + x + ", shape = " + shape + |
| ", scale = 1.0"; |
| final double expected = Double.parseDouble(tokens[1]); |
| final double ulp = FastMath.ulp(expected); |
| final double actualOld = density(x, shape, 1.0); |
| final double actualNew = distribution.density(x); |
| final double errOld, errNew; |
| errOld = FastMath.abs((actualOld - expected) / ulp); |
| errNew = FastMath.abs((actualNew - expected) / ulp); |
| |
| if (Double.isNaN(actualOld) || Double.isInfinite(actualOld)) { |
| Assert.assertFalse(msg, Double.isNaN(actualNew)); |
| Assert.assertFalse(msg, Double.isInfinite(actualNew)); |
| statNewOF.addValue(errNew); |
| } else { |
| statOld.addValue(errOld); |
| statNewNoOF.addValue(errNew); |
| } |
| } |
| if (statOld.getN() != 0) { |
| /* |
| * If no overflow occurs, check that new implementation is |
| * better than old one. |
| */ |
| final StringBuilder sb = new StringBuilder("shape = "); |
| sb.append(shape); |
| sb.append(", scale = 1.0\n"); |
| sb.append("Old implementation\n"); |
| sb.append("------------------\n"); |
| sb.append(statOld.toString()); |
| sb.append("New implementation\n"); |
| sb.append("------------------\n"); |
| sb.append(statNewNoOF.toString()); |
| final String msg = sb.toString(); |
| |
| final double oldMin = statOld.getMin(); |
| final double newMin = statNewNoOF.getMin(); |
| Assert.assertTrue(msg, newMin <= oldMin); |
| |
| final double oldMax = statOld.getMax(); |
| final double newMax = statNewNoOF.getMax(); |
| Assert.assertTrue(msg, newMax <= oldMax); |
| |
| final double oldMean = statOld.getMean(); |
| final double newMean = statNewNoOF.getMean(); |
| Assert.assertTrue(msg, newMean <= oldMean); |
| |
| final double oldSd = statOld.getStandardDeviation(); |
| final double newSd = statNewNoOF.getStandardDeviation(); |
| Assert.assertTrue(msg, newSd <= oldSd); |
| |
| Assert.assertTrue(msg, newMean <= meanNoOF); |
| Assert.assertTrue(msg, newSd <= sdNoOF); |
| } |
| if (statNewOF.getN() != 0) { |
| final double newMean = statNewOF.getMean(); |
| final double newSd = statNewOF.getStandardDeviation(); |
| |
| final StringBuilder sb = new StringBuilder("shape = "); |
| sb.append(shape); |
| sb.append(", scale = 1.0"); |
| sb.append(", max. mean error (ulps) = "); |
| sb.append(meanOF); |
| sb.append(", actual mean error (ulps) = "); |
| sb.append(newMean); |
| sb.append(", max. sd of error (ulps) = "); |
| sb.append(sdOF); |
| sb.append(", actual sd of error (ulps) = "); |
| sb.append(newSd); |
| final String msg = sb.toString(); |
| |
| Assert.assertTrue(msg, newMean <= meanOF); |
| Assert.assertTrue(msg, newSd <= sdOF); |
| } |
| } catch (IOException e) { |
| Assert.fail(e.getMessage()); |
| } finally { |
| in.close(); |
| } |
| } |
| |
| |
| @Test |
| public void testMath753Shape1() throws IOException { |
| doTestMath753(1.0, 1.5, 0.5, 0.0, 0.0, "gamma-distribution-shape-1.csv"); |
| } |
| |
| @Test |
| public void testMath753Shape8() throws IOException { |
| doTestMath753(8.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-8.csv"); |
| } |
| |
| @Test |
| public void testMath753Shape10() throws IOException { |
| doTestMath753(10.0, 1.0, 1.0, 0.0, 0.0, "gamma-distribution-shape-10.csv"); |
| } |
| |
| @Test |
| public void testMath753Shape100() throws IOException { |
| doTestMath753(100.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-100.csv"); |
| } |
| |
| @Test |
| public void testMath753Shape142() throws IOException { |
| doTestMath753(142.0, 3.3, 1.6, 40.0, 40.0, "gamma-distribution-shape-142.csv"); |
| } |
| |
| @Test |
| public void testMath753Shape1000() throws IOException { |
| doTestMath753(1000.0, 1.0, 1.0, 160.0, 220.0, "gamma-distribution-shape-1000.csv"); |
| } |
| } |
