UpperSHalfEstimate.java

  1. package org.drip.sample.gammaincomplete;

  3. import org.drip.function.e2erf.AbramowitzStegun;
  4. import org.drip.function.e2erf.ErrorFunctionAnalytical;
  5. import org.drip.numerical.common.FormatUtil;
  6. import org.drip.service.env.EnvManager;
  7. import org.drip.specialfunction.incompletegamma.UpperEulerIntegral;

  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>UpperSHalfEstimate</i> illustrates the Estimation of the Upper Incomplete Gamma Function using the NIST
  73.  * (2019) Series for s = 0.5. 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 UpperSHalfEstimate
  113. {

  115.     private static final void EulerIntegralComparison (
  116.         final int termCount,
  117.         final double[] zArray)
  118.         throws Exception
  119.     {
  120.         System.out.println ("\t|---------------------------------------||");

  122.         System.out.println ("\t|           TERM COUNT => " + FormatUtil.FormatDouble (termCount, 2, 0, 1.));

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

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

  128.         System.out.println ("\t|            - Integral Estimate        ||");

  130.         System.out.println ("\t|            - erfc Estimate            ||");

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

  134.         AbramowitzStegun erfWinitzki = ErrorFunctionAnalytical.Winitzki2008b();

  136.         for (double z : zArray)
  137.         {
  138.             UpperEulerIntegral upperEulerIntegral = new UpperEulerIntegral (
  139.                 null,
  140.                 z
  141.             );

  143.             System.out.println (
  144.                 "\t|" + FormatUtil.FormatDouble (z, 1, 2, 1.) + " => " +
  145.                 FormatUtil.FormatDouble (upperEulerIntegral.evaluate (0.5), 1, 10, 1.) + " | " +
  146.                 FormatUtil.FormatDouble (Math.sqrt (Math.PI) * (1. - erfWinitzki.evaluate (Math.sqrt (z))), 1, 10, 1.) + " ||"
  147.             );
  148.         }

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

  152.         System.out.println();
  153.     }

  155.     public static final void main (
  156.         final String[] argumentArray)
  157.         throws Exception
  158.     {
  159.         EnvManager.InitEnv ("");

  161.         int termCount = 50;
  162.         double[] zArray =
  163.         {
  164.             1.00,
  165.             0.95,
  166.             0.90,
  167.             0.85,
  168.             0.80,
  169.             0.75,
  170.             0.70,
  171.             0.65,
  172.             0.60,
  173.             0.55,
  174.             0.50,
  175.             0.45,
  176.             0.40,
  177.             0.35,
  178.             0.30,
  179.             0.25,
  180.             0.20,
  181.             0.15,
  182.             0.10,
  183.             0.05,
  184.             0.01,
  185.         };

  187.         EulerIntegralComparison (
  188.             termCount,
  189.             zArray
  190.         );

  192.         EnvManager.TerminateEnv();
  193.     }
  194. }
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