GautschiConvexProperty.java

  1. package org.drip.sample.gamma;

  3. import org.drip.function.definition.R1ToR1Property;
  4. import org.drip.function.definition.R1PropertyVerification;
  5. import org.drip.numerical.common.FormatUtil;
  6. import org.drip.service.env.EnvManager;
  7. import org.drip.specialfunction.property.GammaInequalityLemma;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */

  13. /*!
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  17.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  18.  *      FX, and structured products.
  19.  *  
  20.  *      https://lakshmidrip.github.io/DROP/
  21.  *  
  22.  *  DROP is composed of three main modules:
  23.  *  
  24.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  25.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  26.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  27.  * 
  28.  *  DROP Analytics Core implements libraries for the following:
  29.  *  - Fixed Income Analytics
  30.  *  - Asset Backed Analytics
  31.  *  - XVA Analytics
  32.  *  - Exposure and Margin Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Numerical Core implements libraries for the following:
  39.  *  - Statistical Learning Library
  40.  *  - Numerical Optimizer Library
  41.  *  - Machine Learning Library
  42.  *  - Spline Builder Library
  43.  * 
  44.  *  Documentation for DROP is Spread Over:
  45.  * 
  46.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  47.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  48.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  49.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  50.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  51.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  52.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  53.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  54.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  55.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  56.  * 
  57.  *  Licensed under the Apache License, Version 2.0 (the "License");
  58.  *      you may not use this file except in compliance with the License.
  59.  *   
  60.  *  You may obtain a copy of the License at
  61.  *      http://www.apache.org/licenses/LICENSE-2.0
  62.  *  
  63.  *  Unless required by applicable law or agreed to in writing, software
  64.  *      distributed under the License is distributed on an "AS IS" BASIS,
  65.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  66.  *  
  67.  *  See the License for the specific language governing permissions and
  68.  *      limitations under the License.
  69.  */

  71. /**
  72.  * <i>GautschiConvexProperty</i> demonstrates the Verification of the Gautschi Double-Bound Convex Property
  73.  * of the Gamma Function. The References are:
  74.  * 
  75.  * <br><br>
  76.  *  <ul>
  77.  *      <li>
  78.  *          Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour
  79.  *              Integration Methods, and some Related Results <i>Ramanujan Journal</i> <b>35 (1)</b> 21-110
  80.  *      </li>
  81.  *      <li>
  82.  *          Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly
  83.  *              https://arxiv.org/abs/1703.05349 <b>arXiv</b>
  84.  *      </li>
  85.  *      <li>
  86.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  87.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  88.  *      </li>
  89.  *      <li>
  90.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  91.  *              University Press</b> New York
  92.  *      </li>
  93.  *      <li>
  94.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  95.  *      </li>
  96.  *  </ul>
  97.  *
  98.  *  <br><br>
  99.  *  <ul>
  100.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  101.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  102.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  103.  *      <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>
  104.  *  </ul>
  105.  *
  106.  * @author Lakshmi Krishnamurthy
  107.  */

  109. public class GautschiConvexProperty
  110. {

  112.     private static final void Verifier (
  113.         final double s,
  114.         final double[] zArray)
  115.         throws Exception
  116.     {
  117.         System.out.println ("\t|----------------------------------------------------------------------||");

  119.         System.out.println ("\t|               GAMMA FUNCTION GAUTSCHI CONVEX PROPERTY                ||");

  121.         System.out.println ("\t|                               s = " + FormatUtil.FormatDouble (s, 1, 1, 1.));

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

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

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

  129.         System.out.println ("\t|                - LHS Value                                           ||");

  131.         System.out.println ("\t|                - Middle Value                                        ||");

  133.         System.out.println ("\t|                - RHS Value                                           ||");

  135.         System.out.println ("\t|                - Left Verification Success?                          ||");

  137.         System.out.println ("\t|                - Right Verification Success?                         ||");

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

  141.         R1ToR1Property gautschiLeftProperty = GammaInequalityLemma.GautschiLeft (s);

  143.         R1ToR1Property gautschiRightProperty = GammaInequalityLemma.GautschiRight (s);

  145.         for (double z : zArray)
  146.         {
  147.             R1PropertyVerification leftVerification = gautschiLeftProperty.verify (z);

  149.             R1PropertyVerification rightVerification = gautschiRightProperty.verify (z);

  151.             System.out.println (
  152.                 "\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
  153.                     FormatUtil.FormatDouble (leftVerification.lValue(), 1, 10, 1.) + " | " +
  154.                     FormatUtil.FormatDouble (leftVerification.rValue(), 1, 10, 1.) + " | " +
  155.                     FormatUtil.FormatDouble (rightVerification.rValue(), 1, 10, 1.) + " | " +
  156.                     leftVerification.verified() + " | " +
  157.                     rightVerification.verified() + " ||"
  158.             );
  159.         }

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

  163.         System.out.println();
  164.     }

  166.     public static final void main (
  167.         final String[] argumentArray)
  168.         throws Exception
  169.     {
  170.         EnvManager.InitEnv ("");

  172.         double[] sArray =
  173.         {
  174.             0.1,
  175.             0.2,
  176.             0.3,
  177.             0.4,
  178.             0.5,
  179.             0.6,
  180.             0.7,
  181.             0.8,
  182.             0.9,
  183.         };
  184.         double[] zArray =
  185.         {
  186.             1.5,
  187.             2.0,
  188.             2.5,
  189.             3.0,
  190.             3.5,
  191.             4.0,
  192.             4.5,
  193.             5.0,
  194.             5.5,
  195.             6.0,
  196.             6.5,
  197.             7.0,
  198.             7.5,
  199.             8.0,
  200.             8.5,
  201.             9.0,
  202.             9.5,
  203.         };

  205.         for (double s : sArray)
  206.         {
  207.             Verifier (
  208.                 s,
  209.                 zArray
  210.             );
  211.         }

  213.         EnvManager.TerminateEnv();
  214.     }
  215. }
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