KummerPfaffSecondTransformation.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.definition.RegularHypergeometricEstimator;
  9. import org.drip.specialfunction.hypergeometric.EulerQuadratureEstimator;

  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>KummerPfaffSecondTransformation</i> reconciles the Hyper-geometric Function Estimates using the Euler
  75.  * Integral Representation against Second Pfaff Transformation. The References are:
  76.  * 
  77.  * <br><br>
  78.  *  <ul>
  79.  *      <li>
  80.  *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
  81.  *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
  82.  *      </li>
  83.  *      <li>
  84.  *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
  85.  *              Computation</i> <b>20 (4)</b> 399-417
  86.  *      </li>
  87.  *      <li>
  88.  *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
  89.  *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
  90.  *              293-300
  91.  *      </li>
  92.  *      <li>
  93.  *          National Institute of Standards and Technology (2019): Hyper-geometric Function
  94.  *              https://dlmf.nist.gov/15
  95.  *      </li>
  96.  *      <li>
  97.  *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
  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">Function</a></li>
  106.  *      <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>
  107.  *  </ul>
  108.  *
  109.  * @author Lakshmi Krishnamurthy
  110.  */

  112. public class KummerPfaffSecondTransformation
  113. {

  115.     private static final void Hypergeometric (
  116.         final double a,
  117.         final double b,
  118.         final double c,
  119.         final R2ToR1 logBetaEstimator,
  120.         final int quadratureCount,
  121.         final double[] zArray)
  122.         throws Exception
  123.     {
  124.         RegularHypergeometricEstimator regularHypergeometricEstimator = new EulerQuadratureEstimator (
  125.             new HypergeometricParameters (
  126.                 a,
  127.                 b,
  128.                 c
  129.             ),
  130.             logBetaEstimator,
  131.             quadratureCount
  132.         );

  134.         RegularHypergeometricEstimator regularHypergeometricEstimatorPfaffSecondTransform =
  135.             regularHypergeometricEstimator.albinatePfaffSecond();

  137.         for (double z : zArray)
  138.         {
  139.             System.out.println ("\t| {a=" +
  140.                 FormatUtil.FormatDouble (a, 1, 2, 1., false) + ", b=" +
  141.                 FormatUtil.FormatDouble (b, 1, 2, 1., false) + "; c=" +
  142.                 FormatUtil.FormatDouble (c, 1, 2, 1., false) + "; z=" +
  143.                 FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => " +
  144.                 FormatUtil.FormatDouble (regularHypergeometricEstimator.evaluate (z), 2, 10, 1., false) + " | " +
  145.                 FormatUtil.FormatDouble (regularHypergeometricEstimatorPfaffSecondTransform.evaluate (z), 2, 10, 1., false) + " ||"
  146.             );
  147.         }
  148.     }

  150.     public static final void main (
  151.         final String[] argumentArray)
  152.         throws Exception
  153.     {
  154.         EnvManager.InitEnv ("");

  156.         double[] aArray =
  157.         {
  158.             1.,
  159.             2.,
  160.         };
  161.         double[] bArray =
  162.         {
  163.             3.,
  164.             4.,
  165.         };
  166.         double[] cArray =
  167.         {
  168.             5.,
  169.             6.,
  170.         };
  171.         double[] zArray =
  172.         {
  173.             -1.00,
  174.             -0.75,
  175.             -0.50,
  176.             -0.25,
  177.              0.00,
  178.              0.25,
  179.              0.50,
  180.         };
  181.         int logBetaTermCount = 1000;
  182.         int hypergeometricQuadratureCount = 10000;

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

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

  188.         System.out.println ("\t|       HYPER-GEOMETRIC KUMMER SECOND PFAFF TRANSFORM RECONCILE      ||");

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

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

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

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

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

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

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

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

  206.         for (double a : aArray)
  207.         {
  208.             for (double b : bArray)
  209.             {
  210.                 for (double c : cArray)
  211.                 {
  212.                     Hypergeometric (
  213.                         a,
  214.                         b,
  215.                         c,
  216.                         logBetaEstimator,
  217.                         hypergeometricQuadratureCount,
  218.                         zArray
  219.                     );
  220.                 }
  221.             }
  222.         }

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

  226.         EnvManager.TerminateEnv();
  227.     }
  228. }
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