AlphaPositiveModifiedFirstAsymptote.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.ModifiedFirstFrobeniusSeriesEstimator;
  7. import org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator;
  8. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;

  10. /*
  11.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  12.  */

  14. /*!
  15.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  19.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  20.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  21.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  22.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  23.  *      and computational support.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  32.  * 
  33.  *  DROP Product Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Loan Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Portfolio Core implements libraries for the following:
  39.  *  - Asset Allocation Analytics
  40.  *  - Asset Liability Management Analytics
  41.  *  - Capital Estimation Analytics
  42.  *  - Exposure Analytics
  43.  *  - Margin Analytics
  44.  *  - XVA Analytics
  45.  * 
  46.  *  DROP Computational Core implements libraries for the following:
  47.  *  - Algorithm Support
  48.  *  - Computation Support
  49.  *  - Function Analysis
  50.  *  - Model Validation
  51.  *  - Numerical Analysis
  52.  *  - Numerical Optimizer
  53.  *  - Spline Builder
  54.  *  - Statistical Learning
  55.  * 
  56.  *  Documentation for DROP is Spread Over:
  57.  * 
  58.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  59.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  60.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  61.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  62.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  63.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  64.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  65.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  66.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  67.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  68.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  69.  * 
  70.  *  Licensed under the Apache License, Version 2.0 (the "License");
  71.  *      you may not use this file except in compliance with the License.
  72.  *   
  73.  *  You may obtain a copy of the License at
  74.  *      http://www.apache.org/licenses/LICENSE-2.0
  75.  *  
  76.  *  Unless required by applicable law or agreed to in writing, software
  77.  *      distributed under the License is distributed on an "AS IS" BASIS,
  78.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  79.  *  
  80.  *  See the License for the specific language governing permissions and
  81.  *      limitations under the License.
  82.  */

  84. /**
  85.  * <i>AlphaPositiveModifiedFirstAsymptote</i> illustrates the Alpha Positive Estimation for the Modified
  86.  * Bessel Function of the First Kind. The References are:
  87.  * 
  88.  * <br><br>
  89.  *  <ul>
  90.  *      <li>
  91.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  92.  *              on Mathematics</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
  96.  *              Edition</i> <b>Harcourt</b> San Diego
  97.  *      </li>
  98.  *      <li>
  99.  *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
  100.  *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
  101.  *      </li>
  102.  *      <li>
  103.  *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
  104.  *              Press</b>
  105.  *      </li>
  106.  *      <li>
  107.  *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
  108.  *      </li>
  109.  *  </ul>
  110.  *
  111.  *  <br><br>
  112.  *  <ul>
  113.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  114.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  115.  *      <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>
  116.  *      <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>
  117.  *  </ul>
  118.  *
  119.  * @author Lakshmi Krishnamurthy
  120.  */

  122. public class AlphaPositiveModifiedFirstAsymptote
  123. {

  125.     private static final void BesselI (
  126.         final ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimatorAsymptote,
  127.         final ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator,
  128.         final double[] alphaArray,
  129.         final int zCount)
  130.         throws Exception
  131.     {
  132.         System.out.println ("\t|----------------------------------------------------||");

  134.         System.out.println ("\t|  MODIFIED BESSEL FIRST KIND ASYMPTOTE COMPARISON   ||");

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

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

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

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

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

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

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

  150.         for (double alpha : alphaArray)
  151.         {
  152.             double zWidth = Math.sqrt (1. + alpha) / zCount;

  154.             for (int zIndex = -zCount; zIndex < zCount; ++zIndex)
  155.             {
  156.                 double z = zWidth * (1 + zIndex);

  158.                 String display = "\t| [" +
  159.                     FormatUtil.FormatDouble (alpha, 1, 1, 1., false) + ", " +
  160.                     FormatUtil.FormatDouble (z, 1, 8, 1., false) + "] => " +
  161.                     FormatUtil.FormatDouble (
  162.                         modifiedBesselFirstKindEstimatorAsymptote.bigI (
  163.                             alpha,
  164.                             z
  165.                         ), 1, 10, 1.
  166.                     ) + " | " +
  167.                     FormatUtil.FormatDouble (
  168.                         modifiedBesselFirstKindEstimator.bigI (
  169.                             alpha,
  170.                             z
  171.                         ), 1, 10, 1.
  172.                     ) + " |";

  174.                 System.out.println (display + "|");
  175.             }

  177.             System.out.println ("\t|----------------------------------------------------||");
  178.         }

  180.         System.out.println();
  181.     }

  183.     public static final void main (
  184.         final String[] argumentArray)
  185.         throws Exception
  186.     {
  187.         EnvManager.InitEnv ("");

  189.         int zCount = 10;
  190.         int frobeniusTermCount = 80;
  191.         double[] alphaArray =
  192.         {
  193.              0.0,
  194.              1.0,
  195.              2.0,
  196.              3.0,
  197.              4.0,
  198.              5.0,
  199.              6.0,
  200.              7.0,
  201.              8.0,
  202.              9.0,
  203.             10.0,
  204.         };

  206.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (null);

  208.         BesselI (
  209.             ModifiedBesselFirstKindEstimator.AlphaPositiveAsymptote (gammaEstimator),
  210.             ModifiedFirstFrobeniusSeriesEstimator.Standard (
  211.                 gammaEstimator,
  212.                 frobeniusTermCount
  213.             ),
  214.             alphaArray,
  215.             zCount
  216.         );

  218.         EnvManager.TerminateEnv();
  219.     }
  220. }
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