Definitions.java

  1. package org.drip.specialfunction.gamma;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>Definitions</i> contains all the Definitions and Constants relating to the Gamma Function Family. The
  79.  * References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour
  85.  *              Integration Methods, and some Related Results <i>Ramanujan Journal</i> <b>35 (1)</b> 21-110
  86.  *      </li>
  87.  *      <li>
  88.  *          Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly
  89.  *              https://arxiv.org/abs/1703.05349 <b>arXiv</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  93.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  94.  *      </li>
  95.  *      <li>
  96.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  97.  *              University Press</b> New York
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  101.  *      </li>
  102.  *  </ul>
  103.  *
  104.  *  <br><br>
  105.  *  <ul>
  106.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  107.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  108.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
  109.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/gamma/README.md">Analytic/Series/Integral Gamma Estimators</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class Definitions
  116. {

  118.     /**
  119.      * The Euler-Mascheroni Constant
  120.      */

  122.     public static final double EULER_MASCHERONI = 0.57721566490153286060;

  124.     /**
  125.      * The Gamma Minimum Variate Location
  126.      */

  128.     public static final double MINIMUM_VARIATE_LOCATION = 1.461632144968;

  130.     /**
  131.      * The Gamma Minimum Variate Location
  132.      */

  134.     public static final double MINIMUM_VALUE = 0.885603;

  136.     /**
  137.      * Generate a Table of Built-in E<sub>2</sub> erf/erfc Entries
  138.      * 
  139.      * @return The Table of Built-in E<sub>2</sub> erf/erfc Entries
  140.      */

  142.     public static final java.util.Map<java.lang.Double, java.lang.Double> Table()
  143.     {
  144.         java.util.Map<java.lang.Double, java.lang.Double> builtInEntryTable = new
  145.             java.util.TreeMap<java.lang.Double, java.lang.Double>();

  147.         double sqrtPI = java.lang.Math.sqrt (java.lang.Math.PI);
  148.         
  149.         try
  150.         {
  151.             builtInEntryTable.put (
  152.                 -1.50,
  153.                 4. * sqrtPI / 3.
  154.             );

  156.             builtInEntryTable.put (
  157.                 -0.50,
  158.                 -2. * sqrtPI
  159.             );

  161.             builtInEntryTable.put (
  162.                 0.50,
  163.                 sqrtPI
  164.             );

  166.             builtInEntryTable.put (
  167.                 1.00,
  168.                 1.
  169.             );

  171.             builtInEntryTable.put (
  172.                 1.50,
  173.                 0.50 * sqrtPI
  174.             );

  176.             builtInEntryTable.put (
  177.                 2.00,
  178.                 1.
  179.             );

  181.             builtInEntryTable.put (
  182.                 2.50,
  183.                 0.75 * sqrtPI
  184.             );

  186.             builtInEntryTable.put (
  187.                 3.00,
  188.                 2.
  189.             );

  191.             builtInEntryTable.put (
  192.                 3.50,
  193.                 15. * sqrtPI / 8.
  194.             );

  196.             builtInEntryTable.put (
  197.                 4.00,
  198.                 6.
  199.             );

  201.             return builtInEntryTable;
  202.         }
  203.         catch (java.lang.Exception e)
  204.         {
  205.             e.printStackTrace();
  206.         }

  208.         return null;
  209.     }
  210. }
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