UpperWeissteinEstimate.java

  1. package org.drip.sample.gammaincomplete;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.incompletegamma.UpperEulerIntegral;
  6. import org.drip.specialfunction.incompletegamma.UpperSFixed;

  8. /*
  9.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  10.  */

  12. /*!
  13.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  16.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  17.  *      FX, and structured products.
  18.  *  
  19.  *      https://lakshmidrip.github.io/DROP/
  20.  *  
  21.  *  DROP is composed of three main modules:
  22.  *  
  23.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  24.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  25.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  26.  * 
  27.  *  DROP Analytics Core implements libraries for the following:
  28.  *  - Fixed Income Analytics
  29.  *  - Asset Backed Analytics
  30.  *  - XVA Analytics
  31.  *  - Exposure and Margin Analytics
  32.  * 
  33.  *  DROP Portfolio Core implements libraries for the following:
  34.  *  - Asset Allocation Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Numerical Core implements libraries for the following:
  38.  *  - Statistical Learning Library
  39.  *  - Numerical Optimizer Library
  40.  *  - Machine Learning Library
  41.  *  - Spline Builder Library
  42.  * 
  43.  *  Documentation for DROP is Spread Over:
  44.  * 
  45.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  46.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  47.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  48.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  49.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  50.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  51.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  52.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  53.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  54.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  55.  * 
  56.  *  Licensed under the Apache License, Version 2.0 (the "License");
  57.  *      you may not use this file except in compliance with the License.
  58.  *   
  59.  *  You may obtain a copy of the License at
  60.  *      http://www.apache.org/licenses/LICENSE-2.0
  61.  *  
  62.  *  Unless required by applicable law or agreed to in writing, software
  63.  *      distributed under the License is distributed on an "AS IS" BASIS,
  64.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  65.  *  
  66.  *  See the License for the specific language governing permissions and
  67.  *      limitations under the License.
  68.  */

  70. /**
  71.  * <i>UpperWeissteinEstimate</i> illustrates the Estimation of the Upper Incomplete Gamma Function using the
  72.  * Weisstein Series. The References are:
  73.  * 
  74.  * <br><br>
  75.  *  <ul>
  76.  *      <li>
  77.  *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
  78.  *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
  79.  *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
  80.  *      </li>
  81.  *      <li>
  82.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  83.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  84.  *      </li>
  85.  *      <li>
  86.  *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
  87.  *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
  88.  *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
  89.  *      </li>
  90.  *      <li>
  91.  *          National Institute of Standards and Technology (2019a): Incomplete Gamma and Related Functions
  92.  *              https://dlmf.nist.gov/8
  93.  *      </li>
  94.  *      <li>
  95.  *          Wikipedia (2019): Incomplete Gamma Function
  96.  *              https://en.wikipedia.org/wiki/Incomplete_gamma_function
  97.  *      </li>
  98.  *  </ul>
  99.  *
  100.  *  <br><br>
  101.  *  <ul>
  102.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  103.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  104.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  105.  *      <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>
  106.  *  </ul>
  107.  *
  108.  * @author Lakshmi Krishnamurthy
  109.  */

  111. public class UpperWeissteinEstimate
  112. {

  114.     private static final void EulerIntegralComparison (
  115.         final int termCount,
  116.         final int s,
  117.         final double[] zArray)
  118.         throws Exception
  119.     {
  120.         UpperSFixed upperSZero = UpperSFixed.Weisstein (s);

  122.         String display = "\t|" + FormatUtil.FormatDouble (s, 1, 0, 1.) + " => ";

  124.         for (double z : zArray)
  125.         {
  126.             UpperEulerIntegral upperEulerIntegral = new UpperEulerIntegral (
  127.                 null,
  128.                 z
  129.             );

  131.             display = display + " [" +
  132.                 FormatUtil.FormatDouble (upperEulerIntegral.evaluate (s), 3, 4, 1.) + " -" +
  133.                 FormatUtil.FormatDouble (upperSZero.evaluate (z), 3, 4, 1.) + "] |";
  134.         }

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

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

  145.         int[] sArray = 
  146.         {
  147.              1,
  148.              2,
  149.              3,
  150.              4,
  151.              5,
  152.              6,
  153.              7,
  154.         };
  155.         int termCount = 50;
  156.         double[] zArray =
  157.         {
  158.             8.00,
  159.             6.00,
  160.             4.00,
  161.             2.00,
  162.             0.00,
  163.         };

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

  167.         System.out.println ("\t|                                        UPPER GAMMA INCOMPLETE FUNCTION WEINSTEIN ESTIMATE                                        ||");

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

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

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

  175.         System.out.println ("\t|            - Series Estimate                                                                                                     ||");

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

  179.         for (int s : sArray)
  180.         {
  181.             EulerIntegralComparison (
  182.                 termCount,
  183.                 s,
  184.                 zArray
  185.             );
  186.         }

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

  190.         EnvManager.TerminateEnv();
  191.     }
  192. }
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