LowerRegularizedEstimate.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.LowerRegularized;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  15.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  16.  *      FX, and structured products.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three main modules:
  21.  *  
  22.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  25.  * 
  26.  *  DROP Analytics Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Asset Backed Analytics
  29.  *  - XVA Analytics
  30.  *  - Exposure and Margin Analytics
  31.  * 
  32.  *  DROP Portfolio Core implements libraries for the following:
  33.  *  - Asset Allocation Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Numerical Core implements libraries for the following:
  37.  *  - Statistical Learning Library
  38.  *  - Numerical Optimizer Library
  39.  *  - Machine Learning Library
  40.  *  - Spline Builder Library
  41.  * 
  42.  *  Documentation for DROP is Spread Over:
  43.  * 
  44.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  45.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  46.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  47.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  48.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  49.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  50.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  51.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  52.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  53.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  54.  * 
  55.  *  Licensed under the Apache License, Version 2.0 (the "License");
  56.  *      you may not use this file except in compliance with the License.
  57.  *   
  58.  *  You may obtain a copy of the License at
  59.  *      http://www.apache.org/licenses/LICENSE-2.0
  60.  *  
  61.  *  Unless required by applicable law or agreed to in writing, software
  62.  *      distributed under the License is distributed on an "AS IS" BASIS,
  63.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  64.  *  
  65.  *  See the License for the specific language governing permissions and
  66.  *      limitations under the License.
  67.  */

  69. /**
  70.  * <i>LowerRegularizedEstimate</i> illustrates the Estimation of the Regularized Lower Incomplete Gamma
  71.  * Function using several Techniques. The References are:
  72.  * 
  73.  * <br><br>
  74.  *  <ul>
  75.  *      <li>
  76.  *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
  77.  *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
  78.  *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
  79.  *      </li>
  80.  *      <li>
  81.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  82.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  83.  *      </li>
  84.  *      <li>
  85.  *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
  86.  *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
  87.  *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
  88.  *      </li>
  89.  *      <li>
  90.  *          National Institute of Standards and Technology (2019a): Incomplete Gamma and Related Functions
  91.  *              https://dlmf.nist.gov/8
  92.  *      </li>
  93.  *      <li>
  94.  *          Wikipedia (2019): Incomplete Gamma Function
  95.  *              https://en.wikipedia.org/wiki/Incomplete_gamma_function
  96.  *      </li>
  97.  *  </ul>
  98.  *
  99.  *  <br><br>
  100.  *  <ul>
  101.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  102.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  103.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  104.  *      <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>
  105.  *  </ul>
  106.  *
  107.  * @author Lakshmi Krishnamurthy
  108.  */

  110. public class LowerRegularizedEstimate
  111. {

  113.     private static final void PrintSequence (
  114.         final double s,
  115.         final double[] zArray,
  116.         final LowerRegularized gaussContinuedFraction,
  117.         final LowerRegularized weierstrassLimit,
  118.         final LowerRegularized eulerIntegral,
  119.         final LowerRegularized nist2019)
  120.         throws Exception
  121.     {
  122.         System.out.println ("\t|-------------------------------------------------------------||");

  124.         System.out.println ("\t|    REGULARIZED LOWER INCOMPLETE GAMMA FUNCTION ESTIMATES    ||");

  126.         System.out.println ("\t|                        s => " + FormatUtil.FormatDouble (s, 1, 1, 1.));

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

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

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

  134.         System.out.println ("\t|                - Weierstrass Limit                          ||");

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

  138.         System.out.println ("\t|                - NIST (2019)                                ||");

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

  142.         for (double z : zArray)
  143.         {
  144.             System.out.println (
  145.                 "\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
  146.                 FormatUtil.FormatDouble (
  147.                     gaussContinuedFraction.p (
  148.                         s,
  149.                         z
  150.                     ), 1, 8, 1.
  151.                 ) + " |" +
  152.                 FormatUtil.FormatDouble (
  153.                     weierstrassLimit.p (
  154.                         s,
  155.                         z
  156.                     ), 1, 8, 1.
  157.                 ) + " |" +
  158.                 FormatUtil.FormatDouble (
  159.                     eulerIntegral.p (
  160.                         s,
  161.                         z
  162.                     ), 1, 8, 1.
  163.                 ) + " |" +
  164.                 FormatUtil.FormatDouble (
  165.                     nist2019.p (
  166.                         s,
  167.                         z
  168.                     ), 1, 8, 1.
  169.                 ) + " ||"
  170.             );
  171.         }

  173.         System.out.println ("\t|-------------------------------------------------------------||");
  174.     }

  176.     public static final void main (
  177.         final String[] argumentArray)
  178.         throws Exception
  179.     {
  180.         EnvManager.InitEnv ("");

  182.         int n = 30;
  183.         double[] sArray =
  184.         {
  185.             2.0,
  186.             3.0,
  187.             4.0,
  188.             5.0,
  189.             6.0,
  190.             7.0,
  191.             8.0,
  192.             9.0,
  193.         };
  194.         double[] zArray =
  195.         {
  196.              0.01,
  197.              0.05,
  198.              0.10,
  199.              0.25,
  200.              0.50,
  201.              0.75,
  202.              1.00,
  203.              1.25,
  204.              1.50,
  205.              1.75,
  206.              2.00,
  207.              3.00,
  208.              4.00,
  209.              5.00,
  210.              6.00,
  211.              8.00,
  212.             10.00,
  213.             12.00,
  214.             15.00,
  215.             20.00,
  216.         };

  218.         LowerRegularized nist2019 = LowerRegularized.NIST2019 (n);

  220.         LowerRegularized eulerIntegral = LowerRegularized.EulerIntegral();

  222.         LowerRegularized weierstrassLimit = LowerRegularized.WeierstrassLimit (n);

  224.         LowerRegularized gaussContinuedFraction = LowerRegularized.GaussContinuedFraction (n);

  226.         for (double s : sArray)
  227.         {
  228.             PrintSequence (
  229.                 s,
  230.                 zArray,
  231.                 gaussContinuedFraction,
  232.                 weierstrassLimit,
  233.                 eulerIntegral,
  234.                 nist2019
  235.             );
  236.         }

  238.         EnvManager.TerminateEnv();
  239.     }
  240. }
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