ExponentialConvexProperty.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>ExponentialConvexProperty</i> demonstrates the Verification of the Exponential Convex Property of the
  73.  * 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 ExponentialConvexProperty
  110. {

  112.     private static final void Verifier (
  113.         final double z1,
  114.         final double z2,
  115.         final double[] tArray)
  116.         throws Exception
  117.     {
  118.         System.out.println ("\t|---------------------------------------------------||");

  120.         System.out.println ("\t|    GAMMA FUNCTION EXPONENTIAL CONVEX PROPERTY     ||");

  122.         System.out.println ("\t|                z1 = " + FormatUtil.FormatDouble (z1, 1, 1, 1.));

  124.         System.out.println ("\t|                z2 = " + FormatUtil.FormatDouble (z2, 1, 1, 1.));

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

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

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

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

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

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

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

  140.         R1ToR1Property exponentiallyConvexProperty = GammaInequalityLemma.ExponentiallyConvex (
  141.             z1,
  142.             z2
  143.         );

  145.         for (double t : tArray)
  146.         {
  147.             R1PropertyVerification propertyVerification = exponentiallyConvexProperty.verify (t);

  149.             System.out.println (
  150.                 "\t|" + FormatUtil.FormatDouble (t, 2, 2, 1.) + " => " +
  151.                     FormatUtil.FormatDouble (propertyVerification.lValue(), 3, 10, 1.) + " | " +
  152.                     FormatUtil.FormatDouble (propertyVerification.rValue(), 3, 10, 1.) + " | " +
  153.                     propertyVerification.verified() + " ||"
  154.             );
  155.         }

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

  159.         System.out.println();
  160.     }

  162.     public static final void main (
  163.         final String[] argumentArray)
  164.         throws Exception
  165.     {
  166.         EnvManager.InitEnv ("");

  168.         double[] z1Array =
  169.         {
  170.              1.0,
  171.              4.0,
  172.              7.0,
  173.             10.0
  174.         };
  175.         double[] z2Array =
  176.         {
  177.             0.5,
  178.             3.5,
  179.             6.5,
  180.             9.5,
  181.         };
  182.         double[] tArray =
  183.         {
  184.             0.0,
  185.             0.1,
  186.             0.2,
  187.             0.3,
  188.             0.4,
  189.             0.5,
  190.             0.6,
  191.             0.7,
  192.             0.8,
  193.             0.9,
  194.             1.0,
  195.         };

  197.         for (double z1 : z1Array)
  198.         {
  199.             for (double z2 : z2Array)
  200.             {
  201.                 Verifier (
  202.                     z1,
  203.                     z2,
  204.                     tArray
  205.                 );
  206.             }
  207.         }

  209.         EnvManager.TerminateEnv();
  210.     }
  211. }
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