HighZFirstAsymptote.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.FirstFrobeniusSeriesEstimator;
  6. import org.drip.specialfunction.definition.BesselFirstKindEstimator;
  7. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;

  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>HighZFirstAsymptote</i> illustrates the High z Estimation for the Cylindrical Bessel Function of the
  85.  * First Kind. 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 HighZFirstAsymptote
  122. {

  124.     private static final void BesselJ (
  125.         final BesselFirstKindEstimator besselFirstKindEstimatorAsymptote,
  126.         final BesselFirstKindEstimator besselFirstKindEstimator,
  127.         final double[] alphaArray,
  128.         final double[] zArray)
  129.         throws Exception
  130.     {
  131.         System.out.println ("\t|-----------------------------------------------||");

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

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

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

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

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

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

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

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

  149.         for (double alpha : alphaArray)
  150.         {
  151.             for (double z : zArray)
  152.             {
  153.                 String display = "\t| [" +
  154.                     FormatUtil.FormatDouble (alpha, 1, 2, 1., false) + ", " +
  155.                     FormatUtil.FormatDouble (z, 2, 1, 1., false) + "] => " +
  156.                     FormatUtil.FormatDouble (
  157.                         besselFirstKindEstimatorAsymptote.bigJ (
  158.                             alpha,
  159.                             z
  160.                         ), 1, 10, 1.
  161.                     ) + " | " +
  162.                     FormatUtil.FormatDouble (
  163.                         besselFirstKindEstimator.bigJ (
  164.                             alpha,
  165.                             z
  166.                         ), 1, 10, 1.
  167.                     ) + " |";

  169.                 System.out.println (display + "|");
  170.             }

  172.             System.out.println ("\t|-----------------------------------------------||");
  173.         }

  175.         System.out.println();
  176.     }

  178.     public static final void main (
  179.         final String[] argumentArray)
  180.         throws Exception
  181.     {
  182.         EnvManager.InitEnv ("");

  184.         int frobeniusTermCount = 120;
  185.         double[] zArray =
  186.         {
  187.              0.,
  188.              2.,
  189.              4.,
  190.              6.,
  191.              8.,
  192.             10.,
  193.             12.,
  194.             14.,
  195.             16.,
  196.             18.,
  197.             20.,
  198.             22.,
  199.             24.,
  200.             26.,
  201.             28.,
  202.             30.,
  203.         };
  204.         double[] alphaArray =
  205.         {
  206.             0.00,
  207.             0.25,
  208.             0.50,
  209.             0.75,
  210.             1.00,
  211.             1.25,
  212.             1.50,
  213.             1.75,
  214.             2.00,
  215.         };

  217.         BesselJ (
  218.             BesselFirstKindEstimator.HighZAsymptote(),
  219.             FirstFrobeniusSeriesEstimator.Standard (
  220.                 new EulerIntegralSecondKind (null),
  221.                 frobeniusTermCount
  222.             ),
  223.             alphaArray,
  224.             zArray
  225.         );

  227.         EnvManager.TerminateEnv();
  228.     }
  229. }
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