AsymptoticEstimate.java

  1. package org.drip.sample.digamma;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>AsymptoticEstimate</i> demonstrates the Estimation of the Digamma Function using the Asymptotic Series.
  83.  * The References are:
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
  89.  *              Mathematics</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
  93.  *              Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
  97.  *              Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
  98.  *      </li>
  99.  *      <li>
  100.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  101.  *              University Press</b> New York
  102.  *      </li>
  103.  *      <li>
  104.  *          Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function
  105.  *      </li>
  106.  *  </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  112.  *      <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>
  113.  *      <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>
  114.  *  </ul>
  115.  *
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class AsymptoticEstimate
  120. {

  122.     public static final void main (
  123.         final String[] argumentArray)
  124.         throws Exception
  125.     {
  126.         EnvManager.InitEnv ("");

  128.         int termCount = 1000000;
  129.         double[] zArray =
  130.         {
  131.             0.5,
  132.             1.0,
  133.             1.5,
  134.             2.0,
  135.             2.5,
  136.             3.0,
  137.             3.5,
  138.             4.0,
  139.             4.5,
  140.             5.0,
  141.             5.5,
  142.             6.0,
  143.             6.5,
  144.             7.0,
  145.             7.5,
  146.             8.0,
  147.             8.5,
  148.             9.0,
  149.             9.5,
  150.         };

  152.         CumulativeSeriesEstimator asymptoticSeries = CumulativeSeriesEstimator.Asymptotic();

  154.         CumulativeSeriesEstimator abramowitzStegun2007 =
  155.             CumulativeSeriesEstimator.AbramowitzStegun2007 (termCount);

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

  159.         System.out.println ("\t|  ASYMPTOTIC SERIES DIGAMMA ESTIMATE  ||");

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

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

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

  167.         System.out.println ("\t|        - Abramowitz-Stegun (2007)    ||");

  169.         System.out.println ("\t|        - Asymptotic Series           ||");

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

  173.         for (double z : zArray)
  174.         {
  175.             System.out.println (
  176.                 "\t|" + FormatUtil.FormatDouble (z, 1, 1, 1.) + " => " +
  177.                 FormatUtil.FormatDouble (
  178.                     abramowitzStegun2007.evaluate (z),
  179.                     1, 10, 1.
  180.                 ) + " | " + FormatUtil.FormatDouble (
  181.                     asymptoticSeries.evaluate (z),
  182.                     1, 10, 1.
  183.                 ) + " ||"
  184.             );
  185.         }

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

  189.         EnvManager.TerminateEnv();
  190.     }
  191. }
Created with JaCoCo 0.7.9.201702052155