GaussDougallProperty.java

  1. package org.drip.sample.hypergeometric;

  3. import org.drip.function.definition.R1PropertyVerification;
  4. import org.drip.function.definition.R3ToR1Property;
  5. import org.drip.numerical.common.FormatUtil;
  6. import org.drip.service.env.EnvManager;
  7. import org.drip.specialfunction.property.HypergeometricEqualityLemma;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */

  13. /*!
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  17.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  18.  *      FX, and structured products.
  19.  *  
  20.  *      https://lakshmidrip.github.io/DROP/
  21.  *  
  22.  *  DROP is composed of three main modules:
  23.  *  
  24.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  25.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  26.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  27.  * 
  28.  *  DROP Analytics Core implements libraries for the following:
  29.  *  - Fixed Income Analytics
  30.  *  - Asset Backed Analytics
  31.  *  - XVA Analytics
  32.  *  - Exposure and Margin Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Numerical Core implements libraries for the following:
  39.  *  - Statistical Learning Library
  40.  *  - Numerical Optimizer Library
  41.  *  - Machine Learning Library
  42.  *  - Spline Builder Library
  43.  * 
  44.  *  Documentation for DROP is Spread Over:
  45.  * 
  46.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  47.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  48.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  49.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  50.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  51.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  52.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  53.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  54.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  55.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  56.  * 
  57.  *  Licensed under the Apache License, Version 2.0 (the "License");
  58.  *      you may not use this file except in compliance with the License.
  59.  *   
  60.  *  You may obtain a copy of the License at
  61.  *      http://www.apache.org/licenses/LICENSE-2.0
  62.  *  
  63.  *  Unless required by applicable law or agreed to in writing, software
  64.  *      distributed under the License is distributed on an "AS IS" BASIS,
  65.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  66.  *  
  67.  *  See the License for the specific language governing permissions and
  68.  *      limitations under the License.
  69.  */

  71. /**
  72.  * <i>GaussDougallProperty</i> verifies the Gauss Dougall Identity Property Lemma for z = 1. The References
  73.  * are:
  74.  * 
  75.  * <br><br>
  76.  *  <ul>
  77.  *      <li>
  78.  *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
  79.  *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
  80.  *      </li>
  81.  *      <li>
  82.  *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
  83.  *              Computation</i> <b>20 (4)</b> 399-417
  84.  *      </li>
  85.  *      <li>
  86.  *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
  87.  *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
  88.  *              293-300
  89.  *      </li>
  90.  *      <li>
  91.  *          National Institute of Standards and Technology (2019): Hyper-geometric Function
  92.  *              https://dlmf.nist.gov/15
  93.  *      </li>
  94.  *      <li>
  95.  *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
  96.  *      </li>
  97.  *  </ul>
  98.  *
  99.  *  <br><br>
  100.  *  <ul>
  101.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  102.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  103.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  104.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/hypergeometric/README.md">Estimates of Hyper-geometric Function</a></li>
  105.  *  </ul>
  106.  *
  107.  * @author Lakshmi Krishnamurthy
  108.  */

  110. public class GaussDougallProperty
  111. {

  113.     private static final void Verifier (
  114.         final int m,
  115.         final double b,
  116.         final double c,
  117.         final R3ToR1Property gaussDougallProperty)
  118.         throws Exception
  119.     {
  120.         R1PropertyVerification propertyVerification = gaussDougallProperty.verify (
  121.             m,
  122.             b,
  123.             c
  124.         );

  126.         System.out.println (
  127.             "\t| {" + FormatUtil.FormatDouble (m, 1, 2, 1., false) + ", " +
  128.                 FormatUtil.FormatDouble (b, 1, 2, 1., false) + ", " +
  129.                 FormatUtil.FormatDouble (c, 1, 2, 1., false) + "} => " +
  130.                 FormatUtil.FormatDouble (propertyVerification.lValue(), 1, 10, 1.) + " | " +
  131.                 FormatUtil.FormatDouble (propertyVerification.rValue(), 1, 10, 1.) + " | " +
  132.                 propertyVerification.verified() + " ||"
  133.         );
  134.     }

  136.     public static final void main (
  137.         final String[] argumentArray)
  138.         throws Exception
  139.     {
  140.         EnvManager.InitEnv ("");

  142.         int[] mArray =
  143.         {
  144.             1,
  145.             2,
  146.             3,
  147.             4,
  148.         };
  149.         double[] bArray =
  150.         {
  151.             0.5,
  152.             1.0,
  153.             1.5,
  154.             2.0,
  155.         };
  156.         double[] cArray =
  157.         {
  158.             5.,
  159.             6.,
  160.         };

  162.         R3ToR1Property gaussDougallProperty = HypergeometricEqualityLemma.GaussDougallZPlusOne();

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

  166.         System.out.println ("\t|              GAUSS DOUGALL PROPERTY VERIFIER               ||");

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

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

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

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

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

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

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

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

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

  186.         for (int m : mArray)
  187.         {
  188.             for (double b : bArray)
  189.             {
  190.                 for (double c : cArray)
  191.                 {
  192.                     Verifier (
  193.                         m,
  194.                         b,
  195.                         c,
  196.                         gaussDougallProperty
  197.                     );
  198.                 }
  199.             }
  200.         }

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

  204.         EnvManager.TerminateEnv();
  205.     }
  206. }
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