InfiniteSumSeries.java

  1. package org.drip.specialfunction.loggamma;

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

  114. public class InfiniteSumSeries
  115. {

  117.     /**
  118.      * Construct the R<sup>1</sup> To R<sup>1</sup> Infinite Euler Sum Series
  119.      * 
  120.      * @param termCount Count of the Number of Terms
  121.      * 
  122.      * @return The R<sup>1</sup> To R<sup>1</sup> Infinite Euler Sum Series
  123.      */

  125.     public static final org.drip.numerical.estimation.R1ToR1Series Euler (
  126.         final int termCount)
  127.     {
  128.         try
  129.         {
  130.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  131.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  133.             for (int termIndex = 1; termIndex <= termCount; ++termIndex)
  134.             {
  135.                 termWeightMap.put (
  136.                     termIndex,
  137.                     1.
  138.                 );
  139.             }

  141.             return new org.drip.numerical.estimation.R1ToR1Series (
  142.                 org.drip.specialfunction.loggamma.InfiniteSumSeriesTerm.Euler(),
  143.                 false,
  144.                 termWeightMap
  145.             );
  146.         }
  147.         catch (java.lang.Exception e)
  148.         {
  149.             e.printStackTrace();
  150.         }

  152.         return null;
  153.     }

  155.     /**
  156.      * Construct the R<sup>1</sup> To R<sup>1</sup> Infinite Weierstrass Sum Series
  157.      * 
  158.      * @param termCount Count of the Number of Terms
  159.      * 
  160.      * @return The R<sup>1</sup> To R<sup>1</sup> Infinite Weierstrass Sum Series
  161.      */

  163.     public static final org.drip.numerical.estimation.R1ToR1Series Weierstrass (
  164.         final int termCount)
  165.     {
  166.         try
  167.         {
  168.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  169.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  171.             for (int termIndex = 1; termIndex <= termCount; ++termIndex)
  172.             {
  173.                 termWeightMap.put (
  174.                     termIndex,
  175.                     1.
  176.                 );
  177.             }

  179.             return new org.drip.numerical.estimation.R1ToR1Series (
  180.                 org.drip.specialfunction.loggamma.InfiniteSumSeriesTerm.Weierstrass(),
  181.                 false,
  182.                 termWeightMap
  183.             );
  184.         }
  185.         catch (java.lang.Exception e)
  186.         {
  187.             e.printStackTrace();
  188.         }

  190.         return null;
  191.     }

  193.     /**
  194.      * Construct the R<sup>1</sup> To R<sup>1</sup> Malmsten-Blagouchine Fourier Series
  195.      * 
  196.      * @param termCount Count of the Number of Terms
  197.      * 
  198.      * @return The R<sup>1</sup> To R<sup>1</sup> Malmsten-Blagouchine Fourier Series
  199.      */

  201.     public static final org.drip.numerical.estimation.R1ToR1Series Fourier (
  202.         final int termCount)
  203.     {
  204.         try
  205.         {
  206.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  207.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  209.             for (int termIndex = 1; termIndex <= termCount; ++termIndex)
  210.             {
  211.                 termWeightMap.put (
  212.                     termIndex,
  213.                     1.
  214.                 );
  215.             }

  217.             return new org.drip.numerical.estimation.R1ToR1Series (
  218.                 org.drip.specialfunction.loggamma.InfiniteSumSeriesTerm.Fourier(),
  219.                 false,
  220.                 termWeightMap
  221.             );
  222.         }
  223.         catch (java.lang.Exception e)
  224.         {
  225.             e.printStackTrace();
  226.         }

  228.         return null;
  229.     }

  231.     /**
  232.      * Construct the R<sup>1</sup> To R<sup>1</sup> Blagouchine (2015) Series
  233.      * 
  234.      * @param termCount Count of the Number of Terms
  235.      * 
  236.      * @return The R<sup>1</sup> To R<sup>1</sup> Blagouchine (2015) Series
  237.      */

  239.     public static final org.drip.numerical.estimation.R1ToR1Series Blagouchine2015 (
  240.         final int termCount)
  241.     {
  242.         try
  243.         {
  244.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  245.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  247.             for (int termIndex = 1; termIndex < termCount; ++termIndex)
  248.             {
  249.                 if (2 * termIndex != termCount)
  250.                 {
  251.                     termWeightMap.put (
  252.                         termIndex,
  253.                         1.
  254.                     );
  255.                 }
  256.             }

  258.             return new org.drip.numerical.estimation.R1ToR1Series (
  259.                 org.drip.specialfunction.loggamma.InfiniteSumSeriesTerm.Blagouchine2015(),
  260.                 false,
  261.                 termWeightMap
  262.             );
  263.         }
  264.         catch (java.lang.Exception e)
  265.         {
  266.             e.printStackTrace();
  267.         }

  269.         return null;
  270.     }
  271. }
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