001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     * 
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     * 
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math.special;
018    
019    import org.apache.commons.math.MathException;
020    import org.apache.commons.math.TestUtils;
021    
022    import junit.framework.TestCase;
023    
024    /**
025     * @version $Revision: 778416 $ $Date: 2009-05-25 09:20:07 -0400 (Mon, 25 May 2009) $
026     */
027    public class GammaTest extends TestCase {
028         
029        public GammaTest(String name) {
030            super(name);
031        }
032    
033        private void testRegularizedGamma(double expected, double a, double x) {
034            try {
035                double actualP = Gamma.regularizedGammaP(a, x);
036                double actualQ = Gamma.regularizedGammaQ(a, x);
037                TestUtils.assertEquals(expected, actualP, 10e-15);
038                TestUtils.assertEquals(actualP, 1.0 - actualQ, 10e-15);
039            } catch(MathException ex){
040                fail(ex.getMessage());
041            }
042        }
043    
044        private void testLogGamma(double expected, double x) {
045            double actual = Gamma.logGamma(x);
046            TestUtils.assertEquals(expected, actual, 10e-15);
047        }
048    
049        public void testRegularizedGammaNanPositive() {
050            testRegularizedGamma(Double.NaN, Double.NaN, 1.0);
051        }
052    
053        public void testRegularizedGammaPositiveNan() {
054            testRegularizedGamma(Double.NaN, 1.0, Double.NaN);
055        }
056        
057        public void testRegularizedGammaNegativePositive() {
058            testRegularizedGamma(Double.NaN, -1.5, 1.0);
059        }
060        
061        public void testRegularizedGammaPositiveNegative() {
062            testRegularizedGamma(Double.NaN, 1.0, -1.0);
063        }
064        
065        public void testRegularizedGammaZeroPositive() {
066            testRegularizedGamma(Double.NaN, 0.0, 1.0);
067        }
068        
069        public void testRegularizedGammaPositiveZero() {
070            testRegularizedGamma(0.0, 1.0, 0.0);
071        }
072        
073        public void testRegularizedGammaPositivePositive() {
074            testRegularizedGamma(0.632120558828558, 1.0, 1.0);
075        }
076        
077        public void testLogGammaNan() {
078            testLogGamma(Double.NaN, Double.NaN);
079        }
080        
081        public void testLogGammaNegative() {
082            testLogGamma(Double.NaN, -1.0);
083        }
084        
085        public void testLogGammaZero() {
086            testLogGamma(Double.NaN, 0.0);
087        }
088        
089        public void testLogGammaPositive() {
090            testLogGamma(0.6931471805599457, 3.0);
091        }
092    
093        public void testDigammaLargeArgs() {
094            double eps = 1e-8;
095            assertEquals(4.6001618527380874002, Gamma.digamma(100), eps);
096            assertEquals(3.9019896734278921970, Gamma.digamma(50), eps);
097            assertEquals(2.9705239922421490509, Gamma.digamma(20), eps);
098            assertEquals(2.9958363947076465821, Gamma.digamma(20.5), eps);
099            assertEquals(2.2622143570941481605, Gamma.digamma(10.1), eps);
100            assertEquals(2.1168588189004379233, Gamma.digamma(8.8), eps);
101            assertEquals(1.8727843350984671394, Gamma.digamma(7), eps);
102            assertEquals(0.42278433509846713939, Gamma.digamma(2), eps);
103            assertEquals(-100.56088545786867450, Gamma.digamma(0.01), eps);
104            assertEquals(-4.0390398965921882955, Gamma.digamma(-0.8), eps);
105            assertEquals(4.2003210041401844726, Gamma.digamma(-6.3), eps);
106        }
107    
108        public void testDigammaSmallArgs() {
109            // values for negative powers of 10 from 1 to 30 as computed by webMathematica with 20 digits
110            // see functions.wolfram.com
111            double[] expected = {-10.423754940411076795, -100.56088545786867450, -1000.5755719318103005,
112                    -10000.577051183514335, -100000.57719921568107, -1.0000005772140199687e6, -1.0000000577215500408e7,
113                    -1.0000000057721564845e8, -1.0000000005772156633e9, -1.0000000000577215665e10, -1.0000000000057721566e11,
114                    -1.0000000000005772157e12, -1.0000000000000577216e13, -1.0000000000000057722e14, -1.0000000000000005772e15, -1e+16,
115                    -1e+17, -1e+18, -1e+19, -1e+20, -1e+21, -1e+22, -1e+23, -1e+24, -1e+25, -1e+26,
116                    -1e+27, -1e+28, -1e+29, -1e+30};
117            for (double n = 1; n < 30; n++) {
118                checkRelativeError(String.format("Test %.0f: ", n), expected[(int) (n - 1)], Gamma.digamma(Math.pow(10.0, -n)), 1e-8);
119            }
120        }
121    
122        public void testTrigamma() {
123            double eps = 1e-8;
124            // computed using webMathematica.  For example, to compute trigamma($i) = Polygamma(1, $i), use
125            //
126            // http://functions.wolfram.com/webMathematica/Evaluated.jsp?name=PolyGamma2&plottype=0&vars={%221%22,%22$i%22}&digits=20
127            double[] data = {
128                    1e-4, 1.0000000164469368793e8,
129                    1e-3, 1.0000016425331958690e6,
130                    1e-2, 10001.621213528313220,
131                    1e-1, 101.43329915079275882,
132                    1, 1.6449340668482264365,
133                    2, 0.64493406684822643647,
134                    3, 0.39493406684822643647,
135                    4, 0.28382295573711532536,
136                    5, 0.22132295573711532536,
137                    10, 0.10516633568168574612,
138                    20, 0.051270822935203119832,
139                    50, 0.020201333226697125806,
140                    100, 0.010050166663333571395
141            };
142            for (int i = data.length - 2; i >= 0; i -= 2) {
143                assertEquals(String.format("trigamma %.0f", data[i]), data[i + 1], Gamma.trigamma(data[i]), eps);
144            }
145        }
146    
147        private void checkRelativeError(String msg, double expected, double actual, double tolerance) {
148            assertEquals(msg, expected, actual, Math.abs(tolerance * actual));
149        }
150    }