ERFCCraig1991K15.java

  1. package org.drip.sample.gausskronrod;

  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.GaussKronrodQuadratureGenerator;
  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>ERFCCraig1991K15</i> computes the R<sup>1</sup> Numerical Estimate of the erfc Integrand using the K15
  75.  * Gaussian Integration Quadrature Scheme. The References are:
  76.  * 
  77.  * <br><br>
  78.  *  <ul>
  79.  *      <li>
  80.  *          Holoborodko, P. (2011): Gauss-Kronrod Quadrature Nodes and Weights
  81.  *              https://www.advanpix.com/2011/11/07/gauss-kronrod-quadrature-nodes-weights/
  82.  *      </li>
  83.  *      <li>
  84.  *          Kahaner, D., C. Moler, and S. Nash (1989): <i>Numerical Methods and Software</i> <b>Prentice
  85.  *              Hall</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Laurie, D. (1997): Calculation of Gauss-Kronrod Quadrature Rules <i>Mathematics of
  89.  *              Computation</i> <b>66 (219)</b> 1133-1145
  90.  *      </li>
  91.  *      <li>
  92.  *          Piessens, R., E. de Doncker-Kapenga, C. W. Uberhuber, and D. K. Kahaner (1983): <i>QUADPACK – A
  93.  *              Subroutine Package for Automatic Integration</i> <b>Springer-Verlag</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Wikipedia (2019): Gauss-Kronrod Quadrature Formula
  97.  *              https://en.wikipedia.org/wiki/Gauss%E2%80%93Kronrod_quadrature_formula
  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/sample/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/sample/gausskronrod/README.md">R<sup>1</sup> Gauss-Kronrod Quadrature Schemes</a></li>
  107.  *  </ul>
  108.  *
  109.  * @author Lakshmi Krishnamurthy
  110.  */

  112. public class ERFCCraig1991K15
  113. {

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

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

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

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

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

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

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

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

  135.         System.out.println ("\t|                - K15 Estimate        ||");

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

  139.         for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
  140.         {
  141.             final double x = builtInTableEntry.getKey();

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

  145.             R1ToR1 erfcIntegrand = new R1ToR1 (null)
  146.             {
  147.                 @Override public double evaluate (
  148.                     final double theta)
  149.                     throws java.lang.Exception
  150.                 {
  151.                     if (0. == theta)
  152.                     {
  153.                         return 0.;
  154.                     }

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

  158.                     return 2. * java.lang.Math.exp (-1. * x * x / (sinTheta * sinTheta)) / Math.PI;
  159.                 }
  160.             };

  162.             double erfcEstimate = GaussKronrodQuadratureGenerator.K15 (
  163.                 0.,
  164.                 0.5 * Math.PI
  165.             ).integrate (erfcIntegrand);

  167.             System.out.println (
  168.                 "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
  169.                 FormatUtil.FormatDouble (erfcTable, 1, 9, 1.) + " | " +
  170.                 FormatUtil.FormatDouble (erfcEstimate, 1, 9, 1.) + " ||"
  171.             );
  172.         }

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

  176.         EnvManager.TerminateEnv();
  177.     }
  178. }
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