ModifiedSecondAlphaHalfAsymptote.java

  1. package org.drip.sample.bessel;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.bessel.ModifiedSecondHankelAsymptoteEstimator;
  6. import org.drip.specialfunction.bessel.ModifiedSecondIntegralEstimator;
  7. import org.drip.specialfunction.definition.ModifiedBesselSecondKindEstimator;

  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>ModifiedSecondAlphaHalfAsymptote</i> illustrates the Large z Hankel Asymptote Series Based Estimation
  85.  * for the Modified Bessel Function of the Second Kind, specifically for alpha = 0.5. The References are:
  86.  * 
  87.  * <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  91.  *              on Mathematics</b>
  92.  *      </li>
  93.  *      <li>
  94.  *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
  95.  *              Edition</i> <b>Harcourt</b> San Diego
  96.  *      </li>
  97.  *      <li>
  98.  *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
  99.  *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
  100.  *      </li>
  101.  *      <li>
  102.  *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
  103.  *              Press</b>
  104.  *      </li>
  105.  *      <li>
  106.  *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_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/bessel/README.md">Estimates of the Bessel Functions</a></li>
  116.  *  </ul>
  117.  *
  118.  * @author Lakshmi Krishnamurthy
  119.  */

  121. public class ModifiedSecondAlphaHalfAsymptote
  122. {

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

  132.         System.out.println ("\t|     MODIFIED BESSEL SECOND KIND ALPHA = 0.5 ESTIMATE    ||");

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

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

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

  140.         System.out.println ("\t|                - Integral Estimate                      ||");

  142.         System.out.println ("\t|                - Hankel Asymptote Estimate              ||");

  144.         System.out.println ("\t|                - Exponential Estimate                   ||");

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

  148.         for (double z : zArray)
  149.         {
  150.             System.out.println ("\t| [" + FormatUtil.FormatDouble (z, 2, 1, 1., false) + "] => " +
  151.                 FormatUtil.FormatDouble (
  152.                     modifiedBesselSecondKindEstimatorIntegral.bigK (
  153.                         0.5,
  154.                         z
  155.                     ), 1, 10, 1.
  156.                 ) + " | " +
  157.                 FormatUtil.FormatDouble (
  158.                     modifiedBesselSecondKindEstimatorAsymptote.bigK (
  159.                         0.5,
  160.                         z
  161.                     ), 1, 10, 1.
  162.                 ) + " | " +
  163.                 FormatUtil.FormatDouble (
  164.                     Math.sqrt (0.5 * Math.PI / z) * Math.exp (-z), 1, 10, 1.
  165.                 ) + " ||"
  166.             );
  167.         }

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

  171.         System.out.println();
  172.     }

  174.     public static final void main (
  175.         final String[] argumentArray)
  176.         throws Exception
  177.     {
  178.         EnvManager.InitEnv ("");

  180.         int quadratureCount = 40;
  181.         int hankelAsymptoteTermCount = 5;
  182.         double[] zArray =
  183.         {
  184.                0.5,
  185.                1.0,
  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.               10.0,
  204.               10.5,
  205.               11.0,
  206.         };

  208.         BesselK (
  209.             ModifiedSecondIntegralEstimator.Standard (quadratureCount),
  210.             ModifiedSecondHankelAsymptoteEstimator.Standard (hankelAsymptoteTermCount),
  211.             zArray
  212.         );

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