GesselStantonKoepfProperty2.java

  1. package org.drip.sample.hypergeometric;

  3. import org.drip.function.definition.R1PropertyVerification;
  4. import org.drip.function.definition.R2ToR1Property;
  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>GesselStantonKoepfProperty2</i> verifies the Second Gessel-Stanton-Koepf Identity Property Lemma for
  73.  * Rational Z. The References 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 GesselStantonKoepfProperty2
  111. {

  113.     private static final void Verifier (
  114.         final double a,
  115.         final double[] zArray,
  116.         final R2ToR1Property gesselStantonKoepfProperty)
  117.         throws Exception
  118.     {
  119.         for (double z : zArray)
  120.         {
  121.             R1PropertyVerification propertyVerification = gesselStantonKoepfProperty.verify (
  122.                 a,
  123.                 z
  124.             );

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

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

  142.         double[] aArray =
  143.         {
  144.             -0.10,
  145.             -0.20,
  146.             -0.30,
  147.             -0.40,
  148.             -0.50,
  149.         };
  150.         double[] zArray =
  151.         {
  152.             -Math.PI,
  153.             -0.50 * Math.PI,
  154.             -0.00,
  155.              0.50 * Math.PI,
  156.              Math.PI,
  157.         };

  159.         R2ToR1Property gesselStantonKoepfProperty = HypergeometricEqualityLemma.SecondGesselStantonKoepf();

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

  163.         System.out.println ("\t|    SECOND GESSEL STANTON KOEPF PROPERTY VERIFIER     ||");

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

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

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

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

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

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

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

  179.         for (double a : aArray)
  180.         {
  181.             Verifier (
  182.                 a,
  183.                 zArray,
  184.                 gesselStantonKoepfProperty
  185.             );
  186.         }

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

  190.         EnvManager.TerminateEnv();
  191.     }
  192. }
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