AlzerDifferenceProperty.java

  1. package org.drip.sample.digamma;

  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.DigammaInequalityLemma;

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

  13. /*!
  14.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  18.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  19.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  20.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  21.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  22.  *      and computational support.
  23.  *  
  24.  *      https://lakshmidrip.github.io/DROP/
  25.  *  
  26.  *  DROP is composed of three modules:
  27.  *  
  28.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  29.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  30.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  31.  * 
  32.  *  DROP Product Core implements libraries for the following:
  33.  *  - Fixed Income Analytics
  34.  *  - Loan Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Asset Liability Management Analytics
  40.  *  - Capital Estimation Analytics
  41.  *  - Exposure Analytics
  42.  *  - Margin Analytics
  43.  *  - XVA Analytics
  44.  * 
  45.  *  DROP Computational Core implements libraries for the following:
  46.  *  - Algorithm Support
  47.  *  - Computation Support
  48.  *  - Function Analysis
  49.  *  - Model Validation
  50.  *  - Numerical Analysis
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Statistical Learning
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>AlzerDifferenceProperty</i> demonstrates the Alzer (1997) Difference Property Lemma for Digamma
  85.  * Functions where s is in (0, 1). The References are:
  86.  * 
  87.  * <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
  91.  *              Mathematics</b>
  92.  *      </li>
  93.  *      <li>
  94.  *          Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
  95.  *              Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
  96.  *      </li>
  97.  *      <li>
  98.  *          Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
  99.  *              Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
  100.  *      </li>
  101.  *      <li>
  102.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  103.  *              University Press</b> New York
  104.  *      </li>
  105.  *      <li>
  106.  *          Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function
  107.  *      </li>
  108.  *  </ul>
  109.  *
  110.  *  <br><br>
  111.  *  <ul>
  112.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  113.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  114.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
  115.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/digamma/README.md">Estimates of the Digamma Function</a></li>
  116.  *  </ul>
  117.  *
  118.  * @author Lakshmi Krishnamurthy
  119.  */

  121. public class AlzerDifferenceProperty
  122. {

  124.     private static final void Verifier (
  125.         final double s,
  126.         final double[] zArray)
  127.         throws Exception
  128.     {
  129.         System.out.println ("\t|-----------------------------------------------||");

  131.         System.out.println ("\t|  DIGAMMA FUNCTION ALZER DIFFERENCE PROPERTY   ||");

  133.         System.out.println ("\t|                  s = " + FormatUtil.FormatDouble (s, 1, 2, 1.));

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

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

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

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

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

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

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

  149.         R1ToR1Property alzerDifferenceProperty = DigammaInequalityLemma.AlzerDifference1997 (s);

  151.         for (double z : zArray)
  152.         {
  153.             R1PropertyVerification verification = alzerDifferenceProperty.verify (z);

  155.             System.out.println (
  156.                 "\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
  157.                 FormatUtil.FormatDouble (verification.lValue(), 1, 10, 1.) + " | " +
  158.                 FormatUtil.FormatDouble (verification.rValue(), 1, 10, 1.) + " | " +
  159.                 verification.verified() + " ||"
  160.             );
  161.         }

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

  165.         System.out.println();
  166.     }

  168.     public static final void main (
  169.         final String[] argumentArray)
  170.         throws Exception
  171.     {
  172.         EnvManager.InitEnv ("");

  174.         double[] sArray =
  175.         {
  176.             0.1,
  177.             0.2,
  178.             0.3,
  179.             0.4,
  180.             0.5,
  181.             0.6,
  182.             0.7,
  183.             0.8,
  184.             0.9,
  185.         };
  186.         double[] zArray =
  187.         {
  188.             1.5,
  189.             2.0,
  190.             2.5,
  191.             3.0,
  192.             3.5,
  193.             4.0,
  194.             4.5,
  195.             5.0,
  196.             5.5,
  197.             6.0,
  198.             6.5,
  199.             7.0,
  200.             7.5,
  201.             8.0,
  202.             8.5,
  203.             9.0,
  204.             9.5,
  205.         };

  207.         for (double s : sArray)
  208.         {
  209.             Verifier (
  210.                 s,
  211.                 zArray
  212.             );
  213.         }

  215.         EnvManager.TerminateEnv();
  216.     }
  217. }
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