ModifiedSecondZeroOrder.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.ModifiedSecondIntegralEstimator;
  6. import org.drip.specialfunction.definition.ModifiedBesselSecondKindEstimator;

  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>ModifiedSecondZeroOrder</i> implements the Integral Estimator for the Zero Order Modified Bessel
  84.  * Function of the Second Kind. 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 ModifiedSecondZeroOrder
  121. {

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

  131.         System.out.println ("\t|        ZERO ORDER MODIFIED BESSEL SECOND KIND INTEGRAL ESTIMATE          ||");

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

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

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

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

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

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

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

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

  151.             display = display + " " + FormatUtil.FormatDouble (
  152.                 modifiedBesselSecondKindEstimator.bigK (
  153.                     0.,
  154.                     z
  155.                 ), 2, 6, 1.
  156.             ) + " |";

  158.             System.out.println (display + "|");
  159.         }

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

  163.         System.out.println();
  164.     }

  166.     public static final void main (
  167.         final String[] argumentArray)
  168.         throws Exception
  169.     {
  170.         EnvManager.InitEnv ("");

  172.         int[] quadratureCountArray =
  173.         {
  174.              75,
  175.             575,
  176.             975,
  177.         };
  178.         double[] zArray =
  179.         {
  180.              1.,
  181.              2.,
  182.              3.,
  183.              4.,
  184.              5.,
  185.              6.,
  186.              7.,
  187.              8.,
  188.              9.,
  189.         };

  191.         for (int quadratureCount : quadratureCountArray)
  192.         {
  193.             BesselK (
  194.                 ModifiedSecondIntegralEstimator.ZeroOrder (quadratureCount),
  195.                 quadratureCount,
  196.                 zArray
  197.             );
  198.         }

  200.         EnvManager.TerminateEnv();
  201.     }
  202. }
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