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();
    }
}