HighZSecondAsymptote.java

  1. package org.drip.sample.bessel;

  3. import org.drip.function.definition.R1ToR1;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.specialfunction.bessel.FirstFrobeniusSeriesEstimator;
  7. import org.drip.specialfunction.bessel.SecondNISTSeriesEstimator;
  8. import org.drip.specialfunction.definition.BesselSecondKindEstimator;
  9. import org.drip.specialfunction.digamma.BinetFirstIntegral;
  10. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;

  12. /*
  13.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  14.  */

  16. /*!
  17.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  19.  * 
  20.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  21.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  22.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  23.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  24.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  25.  *      and computational support.
  26.  *  
  27.  *      https://lakshmidrip.github.io/DROP/
  28.  *  
  29.  *  DROP is composed of three modules:
  30.  *  
  31.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  32.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  33.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  34.  * 
  35.  *  DROP Product Core implements libraries for the following:
  36.  *  - Fixed Income Analytics
  37.  *  - Loan Analytics
  38.  *  - Transaction Cost Analytics
  39.  * 
  40.  *  DROP Portfolio Core implements libraries for the following:
  41.  *  - Asset Allocation Analytics
  42.  *  - Asset Liability Management Analytics
  43.  *  - Capital Estimation Analytics
  44.  *  - Exposure Analytics
  45.  *  - Margin Analytics
  46.  *  - XVA Analytics
  47.  * 
  48.  *  DROP Computational Core implements libraries for the following:
  49.  *  - Algorithm Support
  50.  *  - Computation Support
  51.  *  - Function Analysis
  52.  *  - Model Validation
  53.  *  - Numerical Analysis
  54.  *  - Numerical Optimizer
  55.  *  - Spline Builder
  56.  *  - Statistical Learning
  57.  * 
  58.  *  Documentation for DROP is Spread Over:
  59.  * 
  60.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  61.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  62.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  63.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  64.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  65.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  66.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  67.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  68.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  69.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  70.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  71.  * 
  72.  *  Licensed under the Apache License, Version 2.0 (the "License");
  73.  *      you may not use this file except in compliance with the License.
  74.  *   
  75.  *  You may obtain a copy of the License at
  76.  *      http://www.apache.org/licenses/LICENSE-2.0
  77.  *  
  78.  *  Unless required by applicable law or agreed to in writing, software
  79.  *      distributed under the License is distributed on an "AS IS" BASIS,
  80.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  81.  *  
  82.  *  See the License for the specific language governing permissions and
  83.  *      limitations under the License.
  84.  */

  86. /**
  87.  * <i>HighZSecondAsymptote</i> illustrates the High z Estimation for the Cylindrical Bessel Function of the
  88.  * Second Kind. The References are:
  89.  * 
  90.  * <br><br>
  91.  *  <ul>
  92.  *      <li>
  93.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  94.  *              on Mathematics</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
  98.  *              Edition</i> <b>Harcourt</b> San Diego
  99.  *      </li>
  100.  *      <li>
  101.  *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
  102.  *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
  103.  *      </li>
  104.  *      <li>
  105.  *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
  106.  *              Press</b>
  107.  *      </li>
  108.  *      <li>
  109.  *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
  110.  *      </li>
  111.  *  </ul>
  112.  *
  113.  *  <br><br>
  114.  *  <ul>
  115.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  116.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  117.  *      <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>
  118.  *      <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>
  119.  *  </ul>
  120.  *
  121.  * @author Lakshmi Krishnamurthy
  122.  */

  124. public class HighZSecondAsymptote
  125. {

  127.     private static final void BesselY (
  128.         final BesselSecondKindEstimator besselSecondKindEstimatorAsymptote,
  129.         final BesselSecondKindEstimator besselSecondKindEstimator,
  130.         final double[] alphaArray,
  131.         final double[] zArray)
  132.         throws Exception
  133.     {
  134.         System.out.println ("\t|-----------------------------------------------||");

  136.         System.out.println ("\t|   HIGH z BESSEL SECOND ASYMPTOTE COMPARISON   ||");

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

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

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

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

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

  148.         System.out.println ("\t|                - Bessel Frobenius             ||");

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

  152.         for (double alpha : alphaArray)
  153.         {
  154.             for (double z : zArray)
  155.             {
  156.                 String display = "\t| [" +
  157.                     FormatUtil.FormatDouble (alpha, 1, 2, 1., false) + ", " +
  158.                     FormatUtil.FormatDouble (z, 2, 1, 1., false) + "] => " +
  159.                     FormatUtil.FormatDouble (
  160.                         besselSecondKindEstimatorAsymptote.bigY (
  161.                             alpha,
  162.                             z
  163.                         ), 1, 10, 1.
  164.                     ) + " | " +
  165.                     FormatUtil.FormatDouble (
  166.                         besselSecondKindEstimator.bigY (
  167.                             alpha,
  168.                             z
  169.                         ), 1, 10, 1.
  170.                     ) + " |";

  172.                 System.out.println (display + "|");
  173.             }

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

  178.         System.out.println();
  179.     }

  181.     public static final void main (
  182.         final String[] argumentArray)
  183.         throws Exception
  184.     {
  185.         EnvManager.InitEnv ("");

  187.         int besselFirstTermCount = 80;
  188.         int besselSecondTermCount = 80;
  189.         double[] zArray =
  190.         {
  191.              0.,
  192.              2.,
  193.              4.,
  194.              6.,
  195.              8.,
  196.             10.,
  197.             12.,
  198.             14.,
  199.             16.,
  200.             18.,
  201.             20.,
  202.             22.,
  203.             24.,
  204.             26.,
  205.             28.,
  206.             30.,
  207.         };
  208.         double[] alphaArray =
  209.         {
  210.             0.00,
  211.             1.00,
  212.             2.00,
  213.             3.00,
  214.             4.00,
  215.         };

  217.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (null);

  219.         BesselY (
  220.             BesselSecondKindEstimator.HighZAsymptote(),
  221.             SecondNISTSeriesEstimator.Standard (
  222.                 new BinetFirstIntegral (null),
  223.                 gammaEstimator,
  224.                 FirstFrobeniusSeriesEstimator.Standard (
  225.                     gammaEstimator,
  226.                     besselFirstTermCount
  227.                 ),
  228.                 besselSecondTermCount
  229.             ),
  230.             alphaArray,
  231.             zArray
  232.         );

  234.         EnvManager.TerminateEnv();
  235.     }
  236. }
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