ERFCCraig1991GaussLegendre.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.numerical.common.FormatUtil;
  8. import org.drip.numerical.integration.GaussLegendreQuadratureGenerator;
  9. import org.drip.service.env.EnvManager;

  11. /*
  12.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  13.  */

  15. /*!
  16.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  19.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  20.  *      FX, and structured products.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three main modules:
  25.  *  
  26.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  29.  * 
  30.  *  DROP Analytics Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Asset Backed Analytics
  33.  *  - XVA Analytics
  34.  *  - Exposure and Margin Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Transaction Cost Analytics
  39.  * 
  40.  *  DROP Numerical Core implements libraries for the following:
  41.  *  - Statistical Learning Library
  42.  *  - Numerical Optimizer Library
  43.  *  - Machine Learning Library
  44.  *  - Spline Builder Library
  45.  * 
  46.  *  Documentation for DROP is Spread Over:
  47.  * 
  48.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  49.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  50.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  51.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  52.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  53.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  54.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  55.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  56.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  57.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  58.  * 
  59.  *  Licensed under the Apache License, Version 2.0 (the "License");
  60.  *      you may not use this file except in compliance with the License.
  61.  *   
  62.  *  You may obtain a copy of the License at
  63.  *      http://www.apache.org/licenses/LICENSE-2.0
  64.  *  
  65.  *  Unless required by applicable law or agreed to in writing, software
  66.  *      distributed under the License is distributed on an "AS IS" BASIS,
  67.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  68.  *  
  69.  *  See the License for the specific language governing permissions and
  70.  *      limitations under the License.
  71.  */

  73. /**
  74.  * <i>ERFCCraig1991GaussLegendre</i> computes the R<sup>1</sup> Numerical Estimate of the erfc Integrand
  75.  * using the Gauss-Legendre Integration Quadrature Scheme. The References are:
  76.  * 
  77.  * <br><br>
  78.  *  <ul>
  79.  *      <li>
  80.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  81.  *              on Mathematics</b>
  82.  *      </li>
  83.  *      <li>
  84.  *          Gil, A., J. Segura, and N. M. Temme (2007): <i>Numerical Methods for Special Functions</i>
  85.  *              <b>Society for Industrial and Applied Mathematics</b> Philadelphia
  86.  *      </li>
  87.  *      <li>
  88.  *          Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
  89.  *              The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
  90.  *      </li>
  91.  *      <li>
  92.  *          Stoer, J., and R. Bulirsch (2002): <i>Introduction to Numerical Analysis 3rd Edition</i>
  93.  *              <b>Springer</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature
  97.  *      </li>
  98.  *  </ul>
  99.  *
  100.  *  <br><br>
  101.  *  <ul>
  102.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  103.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  104.  *      <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>
  105.  *      <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>
  106.  *  </ul>
  107.  *
  108.  * @author Lakshmi Krishnamurthy
  109.  */

  111. public class ERFCCraig1991GaussLegendre
  112. {

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

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

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

  124.         System.out.println ("\t|                                     Craig 1991 erfc Estimate                                     ||");

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

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

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

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

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

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

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

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

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

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

  146.         for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
  147.         {
  148.             final double x = builtInTableEntry.getKey();

  150.             double erfcTable = builtInTableEntry.getValue().erfc();

  152.             R1ToR1 erfcIntegrand = new R1ToR1 (null)
  153.             {
  154.                 @Override public double evaluate (
  155.                     final double theta)
  156.                     throws java.lang.Exception
  157.                 {
  158.                     if (0. == theta)
  159.                     {
  160.                         return 0.;
  161.                     }

  163.                     double sinTheta = java.lang.Math.sin (theta);

  165.                     return 2. * java.lang.Math.exp (-1. * x * x / (sinTheta * sinTheta)) / Math.PI;
  166.                 }
  167.             };

  169.             double erfcEstimate5P = GaussLegendreQuadratureGenerator.FivePoint (
  170.                 0.,
  171.                 0.5 * Math.PI
  172.             ).integrate (erfcIntegrand);

  174.             double erfcEstimate4P = GaussLegendreQuadratureGenerator.FourPoint (
  175.                 0.,
  176.                 0.5 * Math.PI
  177.             ).integrate (erfcIntegrand);

  179.             double erfcEstimate3P = GaussLegendreQuadratureGenerator.ThreePoint (
  180.                 0.,
  181.                 0.5 * Math.PI
  182.             ).integrate (erfcIntegrand);

  184.             double erfcEstimate2P = GaussLegendreQuadratureGenerator.TwoPoint (
  185.                 0.,
  186.                 0.5 * Math.PI
  187.             ).integrate (erfcIntegrand);

  189.             double erfcEstimate1P = GaussLegendreQuadratureGenerator.OnePoint (
  190.                 0.,
  191.                 0.5 * Math.PI
  192.             ).integrate (erfcIntegrand);

  194.             System.out.println (
  195.                 "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
  196.                 FormatUtil.FormatDouble (erfcTable, 1, 9, 1.) + " | " +
  197.                 FormatUtil.FormatDouble (erfcEstimate5P, 1, 9, 1.) + " | " +
  198.                 FormatUtil.FormatDouble (erfcEstimate4P, 1, 9, 1.) + " | " +
  199.                 FormatUtil.FormatDouble (erfcEstimate3P, 1, 9, 1.) + " | " +
  200.                 FormatUtil.FormatDouble (erfcEstimate2P, 1, 9, 1.) + " | " +
  201.                 FormatUtil.FormatDouble (erfcEstimate1P, 1, 9, 1.) + " ||"
  202.             );
  203.         }

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

  207.         EnvManager.TerminateEnv();
  208.     }
  209. }
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