/*
 * 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.math.special;

import org.apache.commons.math.MathException;
import org.apache.commons.math.TestUtils;

import junit.framework.TestCase;

/**
 * @version $Revision$ $Date$
 */
public class GammaTest extends TestCase {

	public GammaTest(String name) {
		super(name);
	}

	private void testRegularizedGamma(double expected, double a, double x) {
		try {
			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);
		} catch (MathException ex) {
			fail(ex.getMessage());
		}
	}

	private void testLogGamma(double expected, double x) {
		double actual = Gamma.logGamma(x);
		TestUtils.assertEquals(expected, actual, 10e-15);
	}

	public void testRegularizedGammaNanPositive() {
		testRegularizedGamma(Double.NaN, Double.NaN, 1.0);
	}

	public void testRegularizedGammaPositiveNan() {
		testRegularizedGamma(Double.NaN, 1.0, Double.NaN);
	}

	public void testRegularizedGammaNegativePositive() {
		testRegularizedGamma(Double.NaN, -1.5, 1.0);
	}

	public void testRegularizedGammaPositiveNegative() {
		testRegularizedGamma(Double.NaN, 1.0, -1.0);
	}

	public void testRegularizedGammaZeroPositive() {
		testRegularizedGamma(Double.NaN, 0.0, 1.0);
	}

	public void testRegularizedGammaPositiveZero() {
		testRegularizedGamma(0.0, 1.0, 0.0);
	}

	public void testRegularizedGammaPositivePositive() {
		testRegularizedGamma(0.632120558828558, 1.0, 1.0);
	}

	public void testLogGammaNan() {
		testLogGamma(Double.NaN, Double.NaN);
	}

	public void testLogGammaNegative() {
		testLogGamma(Double.NaN, -1.0);
	}

	public void testLogGammaZero() {
		testLogGamma(Double.NaN, 0.0);
	}

	public void testLogGammaPositive() {
		testLogGamma(0.6931471805599457, 3.0);
	}

	public void testDigammaLargeArgs() {
		double eps = 1e-8;
		assertEquals(4.6001618527380874002, Gamma.digamma(100), eps);
		assertEquals(3.9019896734278921970, Gamma.digamma(50), eps);
		assertEquals(2.9705239922421490509, Gamma.digamma(20), eps);
		assertEquals(2.9958363947076465821, Gamma.digamma(20.5), eps);
		assertEquals(2.2622143570941481605, Gamma.digamma(10.1), eps);
		assertEquals(2.1168588189004379233, Gamma.digamma(8.8), eps);
		assertEquals(1.8727843350984671394, Gamma.digamma(7), eps);
		assertEquals(0.42278433509846713939, Gamma.digamma(2), eps);
		assertEquals(-100.56088545786867450, Gamma.digamma(0.01), eps);
		assertEquals(-4.0390398965921882955, Gamma.digamma(-0.8), eps);
		assertEquals(4.2003210041401844726, Gamma.digamma(-6.3), eps);
	}

	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(Math.pow(10.0, -n)), 1e-8);
		}
	}

	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) {
			assertEquals(String.format("trigamma %.0f", data[i]), data[i + 1], Gamma.trigamma(data[i]), eps);
		}
	}

	private void checkRelativeError(String msg, double expected, double actual, double tolerance) {
		assertEquals(msg, expected, actual, Math.abs(tolerance * actual));
	}
}
