NormalIntegrandGaussLaguerreLeft.java

package org.drip.sample.newtoncotes;

import org.drip.function.definition.R1ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.integration.NewtonCotesQuadratureGenerator;
import org.drip.service.env.EnvManager;

/*
 * -*- 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>NormalIntegrandGaussLaguerreLeft</i> computes the R<sup>1</sup> Numerical Estimate of the Normal
 * Integrand using Gauss-Laguerre Transform over the Right Half R<sup>+</sup> Range using the Newton-Cotes
 * Quadrature. The References are:
 * 
 * <br><br>
 * 	<ul>
 * 		<li>
 * 			Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): <i>Frank-Wolfe Bayesian
 * 				Quadrature: Probabilistic Integration with Theoretical Guarantees</i> <b>arXiv</b>
 * 		</li>
 * 		<li>
 * 			Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): <i>Computer Methods for Mathematical
 * 				Computation</i> <b>Prentice Hall</b> Englewood Cliffs NJ
 * 		</li>
 * 		<li>
 * 			Leader, J. J. (2004): <i>Numerical Analysis and Scientific Computation</i> <b>Addison Wesley</b>
 * 		</li>
 * 		<li>
 * 			Stoer, J., and R. Bulirsch (1980): <i>Introduction to Numerical Analysis</i>
 * 				<b>Springer-Verlag</b> New York
 * 		</li>
 * 		<li>
 * 			Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration
 * 		</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/newtoncotes/README.md">R<sup>1</sup> Newton-Cotes Quadrature Schemes</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class NormalIntegrandGaussLaguerreLeft
{

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

		int[] intermediatePointCountArray =
		{
			 20,
			 40,
			 60,
			 80,
			100,
			120,
			140,
			160,
			180,
			200
		};

		R1ToR1 normalDensity = new R1ToR1 (null)
		{
			@Override public double evaluate (
				final double z)
			{
				return Math.exp (-0.5 * z * z) / Math.sqrt (2. * Math.PI);
			}
		};

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

		System.out.println ("\t|   GAUSS LAGUERRE   ||");

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

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

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

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

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

		for (int intermediatePointCount : intermediatePointCountArray)
		{
			System.out.println (
				"\t|" + FormatUtil.FormatDouble (intermediatePointCount, 3, 0, 1.) + " => " +
				FormatUtil.FormatDouble (
					NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (
						0.,
						intermediatePointCount
					).integrate (normalDensity), 1, 8, 1.
				) + " ||"
			);
		}

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

		EnvManager.TerminateEnv();
	}
}