LowerZInfinityAsymptote.java

  1. package org.drip.sample.gammaincomplete;

  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.incompletegamma.LimitAsymptote;
  7. import org.drip.specialfunction.incompletegamma.LowerSFixed;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */

  13. /*!
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  17.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  18.  *      FX, and structured products.
  19.  *  
  20.  *      https://lakshmidrip.github.io/DROP/
  21.  *  
  22.  *  DROP is composed of three main modules:
  23.  *  
  24.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  25.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  26.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  27.  * 
  28.  *  DROP Analytics Core implements libraries for the following:
  29.  *  - Fixed Income Analytics
  30.  *  - Asset Backed Analytics
  31.  *  - XVA Analytics
  32.  *  - Exposure and Margin Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Numerical Core implements libraries for the following:
  39.  *  - Statistical Learning Library
  40.  *  - Numerical Optimizer Library
  41.  *  - Machine Learning Library
  42.  *  - Spline Builder Library
  43.  * 
  44.  *  Documentation for DROP is Spread Over:
  45.  * 
  46.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  47.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  48.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  49.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  50.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  51.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  52.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  53.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  54.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  55.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  56.  * 
  57.  *  Licensed under the Apache License, Version 2.0 (the "License");
  58.  *      you may not use this file except in compliance with the License.
  59.  *   
  60.  *  You may obtain a copy of the License at
  61.  *      http://www.apache.org/licenses/LICENSE-2.0
  62.  *  
  63.  *  Unless required by applicable law or agreed to in writing, software
  64.  *      distributed under the License is distributed on an "AS IS" BASIS,
  65.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  66.  *  
  67.  *  See the License for the specific language governing permissions and
  68.  *      limitations under the License.
  69.  */

  71. /**
  72.  * <i>LowerZInfinityAsymptote</i> illustrates the Asymptotic Behavior of the Lower Incomplete Gamma Function
  73.  * in the Neighborhood of z = Infinity using the Weierstrass Limit Series. The References are:
  74.  * 
  75.  * <br><br>
  76.  *  <ul>
  77.  *      <li>
  78.  *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
  79.  *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
  80.  *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
  81.  *      </li>
  82.  *      <li>
  83.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  84.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  85.  *      </li>
  86.  *      <li>
  87.  *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
  88.  *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
  89.  *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          National Institute of Standards and Technology (2019a): Incomplete Gamma and Related Functions
  93.  *              https://dlmf.nist.gov/8
  94.  *      </li>
  95.  *      <li>
  96.  *          Wikipedia (2019): Incomplete Gamma Function
  97.  *              https://en.wikipedia.org/wiki/Incomplete_gamma_function
  98.  *      </li>
  99.  *  </ul>
  100.  *
  101.  *  <br><br>
  102.  *  <ul>
  103.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  104.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  105.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  106.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gammaincomplete/README.md">Estimates of Incomplete Gamma Functions</a></li>
  107.  *  </ul>
  108.  *
  109.  * @author Lakshmi Krishnamurthy
  110.  */

  112. public class LowerZInfinityAsymptote
  113. {

  115.     private static final void WeierstrassAsymptoteComparison (
  116.         final int termCount,
  117.         final double s,
  118.         final double[] zArray)
  119.         throws Exception
  120.     {
  121.         LowerSFixed lowerSFixed = LowerSFixed.WeierstrassLimit (
  122.             s,
  123.             termCount
  124.         );

  126.         R1ToR1 zInfinityLimitAsymptote = LimitAsymptote.Lower().zInfinity (s);

  128.         String display = "\t|" + FormatUtil.FormatDouble (s, 1, 2, 1.) + " =>";

  130.         for (double z : zArray)
  131.         {
  132.             display = display + " [" +
  133.                 FormatUtil.FormatDouble (lowerSFixed.evaluate (z), 1, 5, 1.) + " -" +
  134.                 FormatUtil.FormatDouble (zInfinityLimitAsymptote.evaluate (z), 1, 5, 1.) + "] |";
  135.         }

  137.         System.out.println (display + "|");
  138.     }

  140.     public static final void main (
  141.         final String[] argumentArray)
  142.         throws Exception
  143.     {
  144.         EnvManager.InitEnv ("");

  146.         int termCount = 50;
  147.         double[] sArray =
  148.         {
  149.             0.10,
  150.             0.20,
  151.             0.30,
  152.             0.40,
  153.             0.50,
  154.             0.60,
  155.             0.70,
  156.             0.80,
  157.             0.90,
  158.             1.00,
  159.             1.20,
  160.             1.40,
  161.             1.60,
  162.             1.80,
  163.             2.00,
  164.         };
  165.         double[] zArray =
  166.         {
  167.             10.,
  168.             20.,
  169.             30.
  170.         };

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

  174.         System.out.println ("\t|                    LOWER INCOMPLETE ASYMPTOTE BEHAVIOR                     ||");

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

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

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

  182.         System.out.println ("\t|            - Weierstrass vs. Asymptote Lower Incomplete Gamma              ||");

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

  186.         for (double s : sArray)
  187.         {
  188.             WeierstrassAsymptoteComparison (
  189.                 termCount,
  190.                 s,
  191.                 zArray
  192.             );
  193.         }

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

  197.         System.out.println();

  199.         EnvManager.TerminateEnv();
  200.     }
  201. }
Created with JaCoCo 0.7.9.201702052155