GaussContinuedFractionProperty.java

  1. package org.drip.sample.hypergeometric;

  3. import org.drip.function.definition.R1PropertyVerification;
  4. import org.drip.function.definition.R1ToR1Property;
  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>GaussContinuedFractionProperty</i> verifies the Gauss Continued Fraction 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 GaussContinuedFractionProperty
  111. {

  113.     private static final void Verifier (
  114.         final double a,
  115.         final double b,
  116.         final double c,
  117.         final double[] zArray,
  118.         final R1ToR1Property gaussContinuedFractionProperty)
  119.         throws Exception
  120.     {
  121.         for (double z : zArray)
  122.         {
  123.             R1PropertyVerification propertyVerification = gaussContinuedFractionProperty.verify (z);

  125.             System.out.println (
  126.                 "\t| {" + FormatUtil.FormatDouble (a, 1, 2, 1., false) + ", " +
  127.                     FormatUtil.FormatDouble (b, 1, 2, 1., false) + ", " +
  128.                     FormatUtil.FormatDouble (c, 1, 2, 1., false) + ", " +
  129.                     FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => " +
  130.                     FormatUtil.FormatDouble (propertyVerification.lValue(), 1, 10, 1.) + " | " +
  131.                     FormatUtil.FormatDouble (propertyVerification.rValue(), 1, 10, 1.) + " | " +
  132.                     propertyVerification.verified() + " ||"
  133.             );
  134.         }
  135.     }

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

  143.         double[] aArray =
  144.         {
  145.             1.0,
  146.             2.0,
  147.             3.0,
  148.             4.0,
  149.             5.0,
  150.         };
  151.         double[] bArray =
  152.         {
  153.             1.0,
  154.             2.0,
  155.         };
  156.         double[] cArray =
  157.         {
  158.             3.0,
  159.             4.0,
  160.             5.0,
  161.         };
  162.         double[] zArray =
  163.         {
  164.             -0.99,
  165.             -0.75,
  166.             -0.50,
  167.             -0.25,
  168.              0.00,
  169.              0.25,
  170.              0.50,
  171.              0.75,
  172.              0.99,
  173.         };

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

  177.         System.out.println ("\t|             GAUSS CONTINUED FRACTION PROPERTY VERIFIER            ||");

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

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

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

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

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

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

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

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

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

  197.         for (double a : aArray)
  198.         {
  199.             for (double b : bArray)
  200.             {
  201.                 for (double c : cArray)
  202.                 {
  203.                     Verifier (
  204.                         a,
  205.                         b,
  206.                         c,
  207.                         zArray,
  208.                         HypergeometricEqualityLemma.GaussContinuedFractionRecursive (
  209.                             a,
  210.                             b,
  211.                             c
  212.                         )
  213.                     );
  214.                 }
  215.             }
  216.         }

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

  220.         EnvManager.TerminateEnv();
  221.     }
  222. }
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