DerivativeEstimate.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>DerivativeEstimate</i> estimates the Hyper-geometric Function Derivative 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 DerivativeEstimate
  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.         final int[] derivativeOrderArray)
  122.         throws Exception
  123.     {
  124.         EulerQuadratureEstimator eulerQuadratureEstimator = new EulerQuadratureEstimator (
  125.             new HypergeometricParameters (
  126.                 a,
  127.                 b,
  128.                 c
  129.             ),
  130.             logBetaEstimator,
  131.             quadratureCount
  132.         );

  134.         for (double z : zArray)
  135.         {
  136.             String display = "\t| {a=" +
  137.                 FormatUtil.FormatDouble (a, 1, 2, 1., false) + ", b=" +
  138.                 FormatUtil.FormatDouble (b, 1, 2, 1., false) + "; c=" +
  139.                 FormatUtil.FormatDouble (c, 1, 2, 1., false) + "; z=" +
  140.                 FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => ";

  142.             for (int derivativeOrder : derivativeOrderArray)
  143.             {
  144.                 display = display + FormatUtil.FormatDouble (
  145.                     eulerQuadratureEstimator.derivative (
  146.                         z,
  147.                         derivativeOrder
  148.                     ), 2, 10, 1.
  149.                 ) + " |";
  150.             }

  152.             System.out.println (display + "|");
  153.         }
  154.     }

  156.     public static final void main (
  157.         final String[] argumentArray)
  158.         throws Exception
  159.     {
  160.         EnvManager.InitEnv ("");

  162.         double[] aArray =
  163.         {
  164.             1.,
  165.             2.,
  166.         };
  167.         double[] bArray =
  168.         {
  169.             3.,
  170.             4.,
  171.         };
  172.         double[] cArray =
  173.         {
  174.             5.,
  175.             6.,
  176.         };
  177.         double[] zArray =
  178.         {
  179.             -1.00,
  180.             -0.75,
  181.             -0.50,
  182.             -0.25,
  183.              0.00,
  184.              0.25,
  185.              0.50,
  186.              0.75,
  187.              1.00
  188.         };
  189.         int[] derivativeOrderArray =
  190.         {
  191.             1,
  192.             2,
  193.             3,
  194.         };
  195.         int logBetaTermCount = 1000;
  196.         int hypergeometricQuadratureCount = 10000;

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

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

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

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

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

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

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

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

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

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

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

  220.         for (double a : aArray)
  221.         {
  222.             for (double b : bArray)
  223.             {
  224.                 for (double c : cArray)
  225.                 {
  226.                     Hypergeometric (
  227.                         a,
  228.                         b,
  229.                         c,
  230.                         logBetaEstimator,
  231.                         hypergeometricQuadratureCount,
  232.                         zArray,
  233.                         derivativeOrderArray
  234.                     );
  235.                 }
  236.             }
  237.         }

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

  241.         EnvManager.TerminateEnv();
  242.     }
  243. }
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