BernsteinBinetBoundProperty.java

  1. package org.drip.sample.digamma;

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

  8. /*
  9.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  10.  */

  12. /*!
  13.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  17.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  18.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  19.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  20.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  21.  *      and computational support.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three modules:
  26.  *  
  27.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  30.  * 
  31.  *  DROP Product Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Loan Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Asset Liability Management Analytics
  39.  *  - Capital Estimation Analytics
  40.  *  - Exposure Analytics
  41.  *  - Margin Analytics
  42.  *  - XVA Analytics
  43.  * 
  44.  *  DROP Computational Core implements libraries for the following:
  45.  *  - Algorithm Support
  46.  *  - Computation Support
  47.  *  - Function Analysis
  48.  *  - Model Validation
  49.  *  - Numerical Analysis
  50.  *  - Numerical Optimizer
  51.  *  - Spline Builder
  52.  *  - Statistical Learning
  53.  * 
  54.  *  Documentation for DROP is Spread Over:
  55.  * 
  56.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  57.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  58.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  59.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  60.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  61.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  62.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  63.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  64.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  65.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  66.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  67.  * 
  68.  *  Licensed under the Apache License, Version 2.0 (the "License");
  69.  *      you may not use this file except in compliance with the License.
  70.  *   
  71.  *  You may obtain a copy of the License at
  72.  *      http://www.apache.org/licenses/LICENSE-2.0
  73.  *  
  74.  *  Unless required by applicable law or agreed to in writing, software
  75.  *      distributed under the License is distributed on an "AS IS" BASIS,
  76.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  77.  *  
  78.  *  See the License for the specific language governing permissions and
  79.  *      limitations under the License.
  80.  */

  82. /**
  83.  * <i>BernsteinBinetBoundProperty</i> demonstrates the Estimation of the Bernstein-Binet Bounds of the
  84.  * Digamma Function. The References are:
  85.  * 
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
  90.  *              Mathematics</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
  94.  *              Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
  98.  *              Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
  99.  *      </li>
  100.  *      <li>
  101.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  102.  *              University Press</b> New York
  103.  *      </li>
  104.  *      <li>
  105.  *          Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  113.  *      <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>
  114.  *      <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>
  115.  *  </ul>
  116.  *
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class BernsteinBinetBoundProperty
  121. {

  123.     private static final void Verifier (
  124.         final double z)
  125.         throws Exception
  126.     {
  127.         R1PropertyVerification leftVerification = DigammaInequalityLemma.BernsteinBinetLeftBound().verify (z);

  129.         R1PropertyVerification rightVerification = DigammaInequalityLemma.BernsteinBinetRightBound().verify (z);

  131.         System.out.println (
  132.             "\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
  133.                 FormatUtil.FormatDouble (leftVerification.lValue(), 1, 10, 1.) + " | " +
  134.                 FormatUtil.FormatDouble (leftVerification.rValue(), 1, 10, 1.) + " | " +
  135.                 FormatUtil.FormatDouble (rightVerification.rValue(), 1, 10, 1.) + " | " +
  136.                 leftVerification.verified() + " | " +
  137.                 rightVerification.verified() + " ||"
  138.         );
  139.     }

  141.     public static final void main (
  142.         final String[] argumentArray)
  143.         throws Exception
  144.     {
  145.         EnvManager.InitEnv ("");

  147.         double[] zArray =
  148.         {
  149.             0.25,
  150.             0.50,
  151.             0.75,
  152.             1.00,
  153.             1.25,
  154.             1.50,
  155.             2.00,
  156.             2.50,
  157.             3.00,
  158.             3.50,
  159.             4.00,
  160.             4.50,
  161.             5.00,
  162.             5.50,
  163.             6.00,
  164.             6.50,
  165.             7.00,
  166.             7.50,
  167.             8.00,
  168.             8.50,
  169.             9.00,
  170.             9.50,
  171.         };
  172.         System.out.println ("\t|----------------------------------------------------------------------||");

  174.         System.out.println ("\t|           DIGAMMA FUNCTION BERNSTEIN-BINET BOUND PROPERTY            ||");

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

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

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

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

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

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

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

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

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

  194.         for (double z : zArray)
  195.         {
  196.             Verifier (z);
  197.         }

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

  201.         EnvManager.TerminateEnv();
  202.     }
  203. }
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