ComparativeEstimate.java

  1. package org.drip.sample.gamma;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  6. import org.drip.specialfunction.gamma.LogReciprocal;
  7. import org.drip.specialfunction.gamma.NemesAnalytic;
  8. import org.drip.specialfunction.gamma.RamanujanSeries;
  9. import org.drip.specialfunction.gamma.StirlingSeries;
  10. import org.drip.specialfunction.gamma.WindschitlTothAnalytic;
  11. import org.drip.specialfunction.loggamma.BinetIntegralFirstKindEstimator;
  12. import org.drip.specialfunction.loggamma.BinetIntegralSecondKindEstimator;
  13. import org.drip.specialfunction.loggamma.InfiniteSumEstimator;

  15. /*
  16.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  17.  */

  19. /*!
  20.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  21.  * 
  22.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  23.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  24.  *      FX, and structured products.
  25.  *  
  26.  *      https://lakshmidrip.github.io/DROP/
  27.  *  
  28.  *  DROP is composed of three main modules:
  29.  *  
  30.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  31.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  32.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  33.  * 
  34.  *  DROP Analytics Core implements libraries for the following:
  35.  *  - Fixed Income Analytics
  36.  *  - Asset Backed Analytics
  37.  *  - XVA Analytics
  38.  *  - Exposure and Margin Analytics
  39.  * 
  40.  *  DROP Portfolio Core implements libraries for the following:
  41.  *  - Asset Allocation Analytics
  42.  *  - Transaction Cost Analytics
  43.  * 
  44.  *  DROP Numerical Core implements libraries for the following:
  45.  *  - Statistical Learning Library
  46.  *  - Numerical Optimizer Library
  47.  *  - Machine Learning Library
  48.  *  - Spline Builder Library
  49.  * 
  50.  *  Documentation for DROP is Spread Over:
  51.  * 
  52.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  53.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  54.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>ComparativeEstimate</i> demonstrates the Comparisons across several Estimation Techniques of the Gamma
  79.  * Function. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour
  85.  *              Integration Methods, and some Related Results <i>Ramanujan Journal</i> <b>35 (1)</b> 21-110
  86.  *      </li>
  87.  *      <li>
  88.  *          Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly
  89.  *              https://arxiv.org/abs/1703.05349 <b>arXiv</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  93.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  94.  *      </li>
  95.  *      <li>
  96.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  97.  *              University Press</b> New York
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  101.  *      </li>
  102.  *  </ul>
  103.  *
  104.  *  <br><br>
  105.  *  <ul>
  106.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  107.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  108.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  109.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gamma/README.md">Integrand Estimates of Gamma Functions</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class ComparativeEstimate
  116. {

  118.     public static final void main (
  119.         final String[] argumentArray)
  120.         throws Exception
  121.     {
  122.         EnvManager.InitEnv ("");

  124.         int eulerTermCount = 1638400;
  125.         int weierstrassTermCount = 1638400;
  126.         double[] sArray =
  127.         {
  128.             0.01000,
  129.             0.05000,
  130.             0.10000,
  131.             0.15000,
  132.             0.20000,
  133.             0.25000,
  134.             0.30000,
  135.             0.35000,
  136.             0.40000,
  137.             0.45000,
  138.             0.50000,
  139.             0.60000,
  140.             0.70000,
  141.             0.80000,
  142.             0.90000,
  143.             1.00000,
  144.             1.10000,
  145.             1.20000,
  146.             1.30000,
  147.             1.40000,
  148.             1.46163,
  149.             1.50000,
  150.             2.00000,
  151.             2.50000,
  152.             3.00000,
  153.             3.50000,
  154.             4.00000,
  155.             4.50000,
  156.             5.00000,
  157.             5.50000,
  158.             6.00000,
  159.             6.50000,
  160.             7.00000,
  161.         };

  163.         StirlingSeries factorial = new StirlingSeries (null);

  165.         NemesAnalytic nemesGamma = new NemesAnalytic (null);

  167.         LogReciprocal logReciprocal = new LogReciprocal (null);

  169.         RamanujanSeries ramanujanGamma = new RamanujanSeries (null);

  171.         WindschitlTothAnalytic windschitlTothGamma = new WindschitlTothAnalytic (null);

  173.         InfiniteSumEstimator eulerInfiniteProduct = InfiniteSumEstimator.Euler (eulerTermCount);

  175.         BinetIntegralFirstKindEstimator binetIntegralFirstKind = new BinetIntegralFirstKindEstimator (null);

  177.         BinetIntegralSecondKindEstimator binetIntegralSecondKind = new BinetIntegralSecondKindEstimator (null);

  179.         EulerIntegralSecondKind eulerIntegralSecondKind = new EulerIntegralSecondKind (null);

  181.         InfiniteSumEstimator weierstrassInfiniteProduct = InfiniteSumEstimator.Weierstrass (weierstrassTermCount);

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

  185.         System.out.println ("\t|                                                               GAMMA FUNCTION ESTIMATE                                                                ||");

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

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

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

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

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

  197.         System.out.println ("\t|                - Euler Infinite Product Series                                                                                                       ||");

  199.         System.out.println ("\t|                - Weierstrass Infinite Product Series                                                                                                 ||");

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

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

  205.         System.out.println ("\t|                - Euler Integral Second Kind                                                                                                          ||");

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

  209.         System.out.println ("\t|                - Binet Integral First Kind                                                                                                           ||");

  211.         System.out.println ("\t|                - Binet Integral Second Kind                                                                                                          ||");

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

  215.         for (double s : sArray)
  216.         {
  217.             System.out.println (
  218.                 "\t|" + FormatUtil.FormatDouble (s, 1, 5, 1.) + " => " +
  219.                 FormatUtil.FormatDouble (windschitlTothGamma.evaluate (s), 3, 6, 1.) + " | " +
  220.                 FormatUtil.FormatDouble (nemesGamma.evaluate (s), 3, 6, 1.) + " | " +
  221.                 FormatUtil.FormatDouble (Math.exp (eulerInfiniteProduct.evaluate (s)), 3, 6, 1.) + " | " +
  222.                 FormatUtil.FormatDouble (Math.exp (weierstrassInfiniteProduct.evaluate (s)), 3, 6, 1.) + " | " +
  223.                 FormatUtil.FormatDouble (ramanujanGamma.evaluate (s), 3, 6, 1.) + " | " +
  224.                 FormatUtil.FormatDouble (factorial.evaluate (s), 3, 6, 1.) + " | " +
  225.                 FormatUtil.FormatDouble (eulerIntegralSecondKind.evaluate (s), 3, 6, 1.) + " | " +
  226.                 FormatUtil.FormatDouble (logReciprocal.evaluate (s), 3, 6, 1.) + " | " +
  227.                 FormatUtil.FormatDouble (Math.exp (binetIntegralFirstKind.evaluate (s)), 3, 6, 1.) + " | " +
  228.                 FormatUtil.FormatDouble (Math.exp (binetIntegralSecondKind.evaluate (s)), 3, 6, 1.) + " ||"
  229.             );
  230.         }

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

  234.         EnvManager.TerminateEnv();
  235.     }
  236. }
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