EulerQuadratureEstimate.java

  1. package org.drip.sample.hypergeometric;

  3. import org.drip.function.definition.R2ToR1;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.specialfunction.beta.LogGammaEstimator;
  7. import org.drip.specialfunction.definition.HypergeometricParameters;
  8. import org.drip.specialfunction.hypergeometric.EulerQuadratureEstimator;

  10. /*
  11.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  12.  */

  14. /*!
  15.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  18.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  19.  *      FX, and structured products.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three main modules:
  24.  *  
  25.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  28.  * 
  29.  *  DROP Analytics Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Asset Backed Analytics
  32.  *  - XVA Analytics
  33.  *  - Exposure and Margin Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Transaction Cost Analytics
  38.  * 
  39.  *  DROP Numerical Core implements libraries for the following:
  40.  *  - Statistical Learning Library
  41.  *  - Numerical Optimizer Library
  42.  *  - Machine Learning Library
  43.  *  - Spline Builder Library
  44.  * 
  45.  *  Documentation for DROP is Spread Over:
  46.  * 
  47.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  48.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  49.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  50.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  51.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  52.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  53.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  54.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  55.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  56.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  57.  * 
  58.  *  Licensed under the Apache License, Version 2.0 (the "License");
  59.  *      you may not use this file except in compliance with the License.
  60.  *   
  61.  *  You may obtain a copy of the License at
  62.  *      http://www.apache.org/licenses/LICENSE-2.0
  63.  *  
  64.  *  Unless required by applicable law or agreed to in writing, software
  65.  *      distributed under the License is distributed on an "AS IS" BASIS,
  66.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  67.  *  
  68.  *  See the License for the specific language governing permissions and
  69.  *      limitations under the License.
  70.  */

  72. /**
  73.  * <i>EulerQuadratureEstimate</i> estimates the Hyper-geometric Function using the Euler Integral
  74.  * Representation. The References are:
  75.  * 
  76.  * <br><br>
  77.  *  <ul>
  78.  *      <li>
  79.  *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
  80.  *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
  81.  *      </li>
  82.  *      <li>
  83.  *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
  84.  *              Computation</i> <b>20 (4)</b> 399-417
  85.  *      </li>
  86.  *      <li>
  87.  *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
  88.  *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
  89.  *              293-300
  90.  *      </li>
  91.  *      <li>
  92.  *          National Institute of Standards and Technology (2019): Hyper-geometric Function
  93.  *              https://dlmf.nist.gov/15
  94.  *      </li>
  95.  *      <li>
  96.  *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
  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/sample/README.md">Function</a></li>
  105.  *      <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>
  106.  *  </ul>
  107.  *
  108.  * @author Lakshmi Krishnamurthy
  109.  */

  111. public class EulerQuadratureEstimate
  112. {

  114.     private static final void Hypergeometric (
  115.         final double a,
  116.         final double b,
  117.         final double c,
  118.         final R2ToR1 logBetaEstimator,
  119.         final int quadratureCount,
  120.         final double[] zArray)
  121.         throws Exception
  122.     {
  123.         EulerQuadratureEstimator eulerQuadratureEstimator = new EulerQuadratureEstimator (
  124.             new HypergeometricParameters (
  125.                 a,
  126.                 b,
  127.                 c
  128.             ),
  129.             logBetaEstimator,
  130.             quadratureCount
  131.         );

  133.         for (double z : zArray)
  134.         {
  135.             System.out.println ("\t| {a=" +
  136.                 FormatUtil.FormatDouble (a, 1, 2, 1., false) + ", b=" +
  137.                 FormatUtil.FormatDouble (b, 1, 2, 1., false) + "; c=" +
  138.                 FormatUtil.FormatDouble (c, 1, 2, 1., false) + "; z=" +
  139.                 FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => " +
  140.                 FormatUtil.FormatDouble (eulerQuadratureEstimator.evaluate (z), 2, 10, 1., false) + " ||"
  141.             );
  142.         }
  143.     }

  145.     public static final void main (
  146.         final String[] argumentArray)
  147.         throws Exception
  148.     {
  149.         EnvManager.InitEnv ("");

  151.         double[] aArray =
  152.         {
  153.             1.,
  154.             2.,
  155.         };
  156.         double[] bArray =
  157.         {
  158.             3.,
  159.             4.,
  160.         };
  161.         double[] cArray =
  162.         {
  163.             5.,
  164.             6.,
  165.         };
  166.         double[] zArray =
  167.         {
  168.             -1.00,
  169.             -0.75,
  170.             -0.50,
  171.             -0.25,
  172.              0.00,
  173.              0.25,
  174.              0.50,
  175.              0.75,
  176.              1.00
  177.         };
  178.         int logBetaTermCount = 1000;
  179.         int hypergeometricQuadratureCount = 10000;

  181.         R2ToR1 logBetaEstimator = LogGammaEstimator.Weierstrass (logBetaTermCount);

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

  185.         System.out.println ("\t| HYPER-GEOMETRIC FUNCTION EULER QUADRATURE ESTIMATE ||");

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

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

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

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

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

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

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

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

  203.         for (double a : aArray)
  204.         {
  205.             for (double b : bArray)
  206.             {
  207.                 for (double c : cArray)
  208.                 {
  209.                     Hypergeometric (
  210.                         a,
  211.                         b,
  212.                         c,
  213.                         logBetaEstimator,
  214.                         hypergeometricQuadratureCount,
  215.                         zArray
  216.                     );
  217.                 }
  218.             }
  219.         }

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

  223.         EnvManager.TerminateEnv();
  224.     }
  225. }
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