KummerConfluentEstimate.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.ConfluentHypergeometricEstimator;
  8. import org.drip.specialfunction.definition.HypergeometricParameters;
  9. import org.drip.specialfunction.derived.Kummer;
  10. import org.drip.specialfunction.hypergeometric.EulerQuadratureEstimator;

  12. /*
  13.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  14.  */

  16. /*!
  17.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  18.  * 
  19.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  20.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  21.  *      FX, and structured products.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three main modules:
  26.  *  
  27.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  30.  * 
  31.  *  DROP Analytics Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Asset Backed Analytics
  34.  *  - XVA Analytics
  35.  *  - Exposure and Margin Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Transaction Cost Analytics
  40.  * 
  41.  *  DROP Numerical Core implements libraries for the following:
  42.  *  - Statistical Learning Library
  43.  *  - Numerical Optimizer Library
  44.  *  - Machine Learning Library
  45.  *  - Spline Builder Library
  46.  * 
  47.  *  Documentation for DROP is Spread Over:
  48.  * 
  49.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  50.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  51.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  52.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  53.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  54.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  55.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  56.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  57.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  58.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  59.  * 
  60.  *  Licensed under the Apache License, Version 2.0 (the "License");
  61.  *      you may not use this file except in compliance with the License.
  62.  *   
  63.  *  You may obtain a copy of the License at
  64.  *      http://www.apache.org/licenses/LICENSE-2.0
  65.  *  
  66.  *  Unless required by applicable law or agreed to in writing, software
  67.  *      distributed under the License is distributed on an "AS IS" BASIS,
  68.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  69.  *  
  70.  *  See the License for the specific language governing permissions and
  71.  *      limitations under the License.
  72.  */

  74. /**
  75.  * <i>KummerConfluentEstimate</i> estimates the Kummer's Confluent Hyper-geometric Function. The References
  76.  * are:
  77.  * 
  78.  * <br><br>
  79.  *  <ul>
  80.  *      <li>
  81.  *          Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series <i>SIAM Journal
  82.  *              on Mathematical Analysis</i> <b>13 (2)</b> 295-308
  83.  *      </li>
  84.  *      <li>
  85.  *          Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation <i>Journal of Symbolic
  86.  *              Computation</i> <b>20 (4)</b> 399-417
  87.  *      </li>
  88.  *      <li>
  89.  *          Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the
  90.  *              Sum of a (_2^3)F(a,b;c;z) <i>Journal of Computational and Applied Mathematics</i> <b>72</b>
  91.  *              293-300
  92.  *      </li>
  93.  *      <li>
  94.  *          National Institute of Standards and Technology (2019): Hyper-geometric Function
  95.  *              https://dlmf.nist.gov/15
  96.  *      </li>
  97.  *      <li>
  98.  *          Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
  99.  *      </li>
  100.  *  </ul>
  101.  *
  102.  *  <br><br>
  103.  *  <ul>
  104.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  105.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  106.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  107.  *      <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>
  108.  *  </ul>
  109.  *
  110.  * @author Lakshmi Krishnamurthy
  111.  */

  113. public class KummerConfluentEstimate
  114. {

  116.     private static final void ConfluentHypergeometric (
  117.         final double a,
  118.         final double b,
  119.         final double c,
  120.         final R2ToR1 logBetaEstimator,
  121.         final int quadratureCount,
  122.         final double[] zArray)
  123.         throws Exception
  124.     {
  125.         ConfluentHypergeometricEstimator confluentHypergeometricEstimator = new Kummer (
  126.             new EulerQuadratureEstimator (
  127.                 new HypergeometricParameters (
  128.                     a,
  129.                     b,
  130.                     c
  131.                 ),
  132.                 logBetaEstimator,
  133.                 quadratureCount
  134.             )
  135.         );

  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, 2, 2, 1., false) + "; c=" +
  142.                 FormatUtil.FormatDouble (c, 2, 2, 1., false) + "; z=" +
  143.                 FormatUtil.FormatDouble (z, 1, 2, 1.) + "} => " +
  144.                 FormatUtil.FormatDouble (confluentHypergeometricEstimator.evaluate (z), 1, 10, 1., false) + " ||"
  145.             );
  146.         }
  147.     }

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

  155.         double[] aArray =
  156.         {
  157.             1.,
  158.             2.,
  159.         };
  160.         double[] cArray =
  161.         {
  162.             15.,
  163.             16.,
  164.         };
  165.         double[] cMinusBArray =
  166.         {
  167.             1.,
  168.             2.,
  169.             3.,
  170.             4.,
  171.             5.,
  172.             6.
  173.         };
  174.         double[] zArray =
  175.         {
  176.             -1.00,
  177.             -0.75,
  178.             -0.50,
  179.             -0.25,
  180.              0.00,
  181.              0.25,
  182.              0.50,
  183.              0.75,
  184.              1.00
  185.         };
  186.         int logBetaTermCount = 1000;
  187.         int hypergeometricQuadratureCount = 10000;

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

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

  193.         System.out.println ("\t| KUMMER CONFLUENT HYPER-GEOMETRIC FUNCTION ESTIMATE  ||");

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

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

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

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

  203.         System.out.println ("\t|                - c Minus b                          ||");

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

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

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

  211.         for (double a : aArray)
  212.         {
  213.             for (double cMinusB : cMinusBArray)
  214.             {
  215.                 for (double c : cArray)
  216.                 {
  217.                     ConfluentHypergeometric (
  218.                         a,
  219.                         c - cMinusB,
  220.                         c,
  221.                         logBetaEstimator,
  222.                         hypergeometricQuadratureCount,
  223.                         zArray
  224.                     );
  225.                 }
  226.             }
  227.         }

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

  231.         EnvManager.TerminateEnv();
  232.     }
  233. }
Created with JaCoCo 0.7.9.201702052155