SecondWatsonEstimate.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.SecondWatsonIntegralEstimator;
  6. import org.drip.specialfunction.definition.BesselSecondKindEstimator;

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

  120. public class SecondWatsonEstimate
  121. {

  123.     private static final void BesselY (
  124.         final BesselSecondKindEstimator besselSecondKindEstimator,
  125.         final int quadratureCount,
  126.         final double[] zArray,
  127.         final double[] alphaArray)
  128.         throws Exception
  129.     {
  130.         System.out.println ("\t|----------------------------------------------------------------------||");

  132.         System.out.println ("\t|           BESSEL SECOND KIND WATSON INTEGER FORM ESTIMATE            ||");

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

  136.         System.out.println ("\t|    Quadrature Term Count => " + quadratureCount);

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

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

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

  144.         System.out.println ("\t|                - Alpha Bessel Estimate Row                           ||");

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

  148.         for (double z : zArray)
  149.         {
  150.             String display = "\t| [" + FormatUtil.FormatDouble (z, 2, 1, 1., false) + "] => ";

  152.             for (double alpha : alphaArray)
  153.             {
  154.                 display = display + " " + FormatUtil.FormatDouble (
  155.                     besselSecondKindEstimator.bigY (
  156.                         alpha,
  157.                         z
  158.                     ), 1, 6, 1.
  159.                 ) + " |";
  160.             }

  162.             System.out.println (display + "|");
  163.         }

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

  167.         System.out.println();
  168.     }

  170.     public static final void main (
  171.         final String[] argumentArray)
  172.         throws Exception
  173.     {
  174.         EnvManager.InitEnv ("");

  176.         int[] quadratureCountArray =
  177.         {
  178.             25,
  179.             50,
  180.             75,
  181.         };
  182.         double[] zArray =
  183.         {
  184.              1.,
  185.              2.,
  186.              3.,
  187.              4.,
  188.              5.,
  189.              6.,
  190.              7.,
  191.              8.,
  192.              9.,
  193.             10.,
  194.             11.,
  195.             12.,
  196.             13.,
  197.             14.,
  198.             15.,
  199.             16.,
  200.             17.,
  201.             18.,
  202.             19.,
  203.             20.,
  204.         };
  205.         double[] alphaArray =
  206.         {
  207.             0.0,
  208.             1.0,
  209.             2.0,
  210.             3.0,
  211.             4.0,
  212.         };

  214.         for (int quadratureCount : quadratureCountArray)
  215.         {
  216.             BesselY (
  217.                 SecondWatsonIntegralEstimator.IntegerForm (quadratureCount),
  218.                 quadratureCount,
  219.                 zArray,
  220.                 alphaArray
  221.             );
  222.         }

  224.         EnvManager.TerminateEnv();
  225.     }
  226. }
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