ERFIntegrandGaussLegendre.java

  1. package org.drip.sample.gaussquadrature;

  3. import java.util.Map;

  5. import org.drip.function.definition.R1ToR1;
  6. import org.drip.function.e2erf.BuiltInEntry;
  7. import org.drip.function.e2erf.ErrorFunction;
  8. import org.drip.numerical.common.FormatUtil;
  9. import org.drip.numerical.integration.GaussLegendreQuadratureGenerator;
  10. import org.drip.service.env.EnvManager;

  12. /*
  13.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  14.  */

  16. /*!
  17.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  18.  * 
  19.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  20.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  21.  *      FX, and structured products.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three main modules:
  26.  *  
  27.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  30.  * 
  31.  *  DROP Analytics Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Asset Backed Analytics
  34.  *  - XVA Analytics
  35.  *  - Exposure and Margin Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Transaction Cost Analytics
  40.  * 
  41.  *  DROP Numerical Core implements libraries for the following:
  42.  *  - Statistical Learning Library
  43.  *  - Numerical Optimizer Library
  44.  *  - Machine Learning Library
  45.  *  - Spline Builder Library
  46.  * 
  47.  *  Documentation for DROP is Spread Over:
  48.  * 
  49.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  50.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  51.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  52.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  53.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  54.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  55.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  56.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  57.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  58.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  59.  * 
  60.  *  Licensed under the Apache License, Version 2.0 (the "License");
  61.  *      you may not use this file except in compliance with the License.
  62.  *   
  63.  *  You may obtain a copy of the License at
  64.  *      http://www.apache.org/licenses/LICENSE-2.0
  65.  *  
  66.  *  Unless required by applicable law or agreed to in writing, software
  67.  *      distributed under the License is distributed on an "AS IS" BASIS,
  68.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  69.  *  
  70.  *  See the License for the specific language governing permissions and
  71.  *      limitations under the License.
  72.  */

  74. /**
  75.  * <i>ERFIntegrandGaussLegendre</i> computes the R<sup>1</sup> Numerical Estimate of the erf Integrand using
  76.  * the Gauss-Legendre Integration Quadrature Scheme. The References are:
  77.  * 
  78.  * <br><br>
  79.  *  <ul>
  80.  *      <li>
  81.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  82.  *              on Mathematics</b>
  83.  *      </li>
  84.  *      <li>
  85.  *          Gil, A., J. Segura, and N. M. Temme (2007): <i>Numerical Methods for Special Functions</i>
  86.  *              <b>Society for Industrial and Applied Mathematics</b> Philadelphia
  87.  *      </li>
  88.  *      <li>
  89.  *          Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
  90.  *              The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
  91.  *      </li>
  92.  *      <li>
  93.  *          Stoer, J., and R. Bulirsch (2002): <i>Introduction to Numerical Analysis 3rd Edition</i>
  94.  *              <b>Springer</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature
  98.  *      </li>
  99.  *  </ul>
  100.  *
  101.  *  <br><br>
  102.  *  <ul>
  103.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  104.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  105.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Analysis</a></li>
  106.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/gaussquadrature/README.md">R<sup>1</sup> Gauss-Legendre Gauss-Lobatto Quadratures</a></li>
  107.  *  </ul>
  108.  *
  109.  * @author Lakshmi Krishnamurthy
  110.  */

  112. public class ERFIntegrandGaussLegendre
  113. {

  115.     public static final void main (
  116.         final String[] argumentArray)
  117.         throws Exception
  118.     {
  119.         EnvManager.InitEnv ("");

  121.         R1ToR1 erfIntegrand = new ErrorFunction (
  122.             null,
  123.             null
  124.         ).integrand();

  126.         Map<Double, BuiltInEntry> builtInTable = BuiltInEntry.Table();

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

  130.         System.out.println ("\t|                                   Gauss Legendre erf Estimate                                    ||");

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

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

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

  138.         System.out.println ("\t|                - Built-in Estimate                                                               ||");

  140.         System.out.println ("\t|                - 5P Estimate                                                                     ||");

  142.         System.out.println ("\t|                - 4P Estimate                                                                     ||");

  144.         System.out.println ("\t|                - 3P Estimate                                                                     ||");

  146.         System.out.println ("\t|                - 2P Estimate                                                                     ||");

  148.         System.out.println ("\t|                - 1P Estimate                                                                     ||");

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

  152.         for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
  153.         {
  154.             final double x = builtInTableEntry.getKey();

  156.             double erfTable = builtInTableEntry.getValue().erf();

  158.             double erfEstimate5P = GaussLegendreQuadratureGenerator.FivePoint (
  159.                 0.,
  160.                 x
  161.             ).integrate (erfIntegrand);

  163.             double erfEstimate4P = GaussLegendreQuadratureGenerator.FourPoint (
  164.                 0.,
  165.                 x
  166.             ).integrate (erfIntegrand);

  168.             double erfEstimate3P = GaussLegendreQuadratureGenerator.ThreePoint (
  169.                 0.,
  170.                 x
  171.             ).integrate (erfIntegrand);

  173.             double erfEstimate2P = GaussLegendreQuadratureGenerator.TwoPoint (
  174.                 0.,
  175.                 x
  176.             ).integrate (erfIntegrand);

  178.             double erfEstimate1P = GaussLegendreQuadratureGenerator.OnePoint (
  179.                 0.,
  180.                 x
  181.             ).integrate (erfIntegrand);

  183.             System.out.println (
  184.                 "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
  185.                 FormatUtil.FormatDouble (erfTable, 1, 9, 1.) + " | " +
  186.                 FormatUtil.FormatDouble (erfEstimate5P, 1, 9, 1.) + " | " +
  187.                 FormatUtil.FormatDouble (erfEstimate4P, 1, 9, 1.) + " | " +
  188.                 FormatUtil.FormatDouble (erfEstimate3P, 1, 9, 1.) + " | " +
  189.                 FormatUtil.FormatDouble (erfEstimate2P, 1, 9, 1.) + " | " +
  190.                 FormatUtil.FormatDouble (erfEstimate1P, 1, 9, 1.) + " ||"
  191.             );
  192.         }

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

  196.         EnvManager.TerminateEnv();
  197.     }
  198. }
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