GammaEstimate1.java

package org.drip.sample.lanczos;

import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.lanczos.ASeriesGenerator;
import org.drip.specialfunction.lanczos.Estimator;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *  	calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
 *  	FX, and structured products.
 *  
 *  	https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three main modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 * 	DROP Analytics Core implements libraries for the following:
 * 	- Fixed Income Analytics
 * 	- Asset Backed Analytics
 * 	- XVA Analytics
 * 	- Exposure and Margin Analytics
 * 
 * 	DROP Portfolio Core implements libraries for the following:
 * 	- Asset Allocation Analytics
 * 	- Transaction Cost Analytics
 * 
 * 	DROP Numerical Core implements libraries for the following:
 * 	- Statistical Learning Library
 * 	- Numerical Optimizer Library
 * 	- Machine Learning Library
 * 	- Spline Builder Library
 * 
 * 	Documentation for DROP is Spread Over:
 * 
 * 	- Main                     => https://lakshmidrip.github.io/DROP/
 * 	- Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 * 	- GitHub                   => https://github.com/lakshmiDRIP/DROP
 * 	- Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 * 	- Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 * 	- Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 * 	- Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 * 	- Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 * 	- JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 * 	- Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed 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.
 */

/**
 * <i>GammaEstimate1</i> illustrates the Generation of the Estimate for the Gamma Function under the Lanczos
 * Scheme. The References are:
 * 
 * <br><br>
 * 	<ul>
 * 		<li>
 * 			Godfrey, P. (2001): Lanczos Implementation of the Gamma Function
 * 				http://www.numericana.com/answer/info/godfrey.htm
 * 		</li>
 * 		<li>
 * 			Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
 * 				The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
 * 		</li>
 * 		<li>
 * 			Pugh, G. R. (2004): <i>An Analysis of the Lanczos Gamma Approximation</i> Ph. D. <b>University of
 * 				British Columbia</b>
 * 		</li>
 * 		<li>
 * 			Toth V. T. (2016): Programmable Calculators – The Gamma Function
 * 				http://www.rskey.org/CMS/index.php/the-library/11
 * 		</li>
 * 		<li>
 * 			Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation
 * 		</li>
 * 	</ul>
 *
 *	<br><br>
 *  <ul>
 *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
 *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/lanczos/README.md">Lanczos Gamma Calculation Scheme Illustration</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class GammaEstimate1
{

	public static final void main (
		final String[] argumentArray)
		throws Exception
	{
		EnvManager.InitEnv ("");

		double z = 1.;
		int[] termCountArray =
		{
			3,
			5,
			7,
			9,
			11,
			13,
			15,
			17,
			19
		};
		int[] gArray = 
		{
			3,
			4,
			5,
			6,
			7,
			8,
			9,
			10
		};

		System.out.println ("\t|------------------------------------------------------------------------------||");

		System.out.println ("\t|                  LANCZOS BASED GAMMA FUNCTION APPROXIMATION                  ||");

		System.out.println ("\t|------------------------------------------------------------------------------||");

		System.out.println ("\t|        L -> R:                                                               ||");

		System.out.println ("\t|                - Term Count                                                  ||");

		System.out.println ("\t|                - Gamma Value for g = 3 -> 10                                 ||");

		System.out.println ("\t|------------------------------------------------------------------------------||");

		for (int termCount : termCountArray)
		{
			String display = "\t|" + FormatUtil.FormatDouble (termCount, 2, 0, 1.) + " => ";

			for (int g : gArray)
			{
				Estimator gammaFunction = new Estimator (
					ASeriesGenerator.Standard (
						g,
						termCount
					),
					null
				);

				display = display + FormatUtil.FormatDouble (gammaFunction.evaluate (z), 3, 2, 1.) + " |";
			}

			System.out.println (display + "|");
		}

		System.out.println ("\t|------------------------------------------------------------------------------||");

		EnvManager.TerminateEnv();
	}
}