InfiniteSumSeriesTerm.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>InfiniteSumSeriesTerm</i> implements a Single Term in the Infinite Series for Log Gamma Estimation. 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/loggamma/README.md">Analytic/Series/Integral Log Gamma Estimators</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class InfiniteSumSeriesTerm
  116. {

  118.     /**
  119.      * Construct the Euler Infinite Sum Series Term for Log Gamma
  120.      * 
  121.      * @return The Euler Infinite Sum Series Term for Log Gamma
  122.      */

  124.     public static final org.drip.numerical.estimation.R1ToR1SeriesTerm Euler()
  125.     {
  126.         try
  127.         {
  128.             return new org.drip.numerical.estimation.R1ToR1SeriesTerm()
  129.             {
  130.                 @Override public double value (
  131.                     final int order,
  132.                     final double z)
  133.                     throws java.lang.Exception
  134.                 {
  135.                     if (0 >= order ||
  136.                         !org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
  137.                     {
  138.                         throw new java.lang.Exception
  139.                             ("InfiniteSumSeriesTerm::Euler::value => Invalid Inputs");
  140.                     }

  142.                     return 0. == z ? 0. : z * java.lang.Math.log (1. + (1. / order)) -
  143.                         java.lang.Math.log (1. + (z / order));
  144.                 }
  145.             };
  146.         }
  147.         catch (java.lang.Exception e)
  148.         {
  149.             e.printStackTrace();
  150.         }

  152.         return null;
  153.     }

  155.     /**
  156.      * Construct the Weierstrass Infinite Sum Series Term for Log Gamma
  157.      * 
  158.      * @return The Weierstrass Infinite Sum Series Term for Log Gamma
  159.      */

  161.     public static final org.drip.numerical.estimation.R1ToR1SeriesTerm Weierstrass()
  162.     {
  163.         try
  164.         {
  165.             return new org.drip.numerical.estimation.R1ToR1SeriesTerm()
  166.             {
  167.                 @Override public double value (
  168.                     final int order,
  169.                     final double z)
  170.                     throws java.lang.Exception
  171.                 {
  172.                     if (0 >= order ||
  173.                         !org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
  174.                     {
  175.                         throw new java.lang.Exception
  176.                             ("InfiniteSumSeriesTerm::Euler::value => Invalid Inputs");
  177.                     }

  179.                     double zOverOrder = z / order;

  181.                     return 0. == z ? 0. : zOverOrder - java.lang.Math.log (1. + zOverOrder);
  182.                 }
  183.             };
  184.         }
  185.         catch (java.lang.Exception e)
  186.         {
  187.             e.printStackTrace();
  188.         }

  190.         return null;
  191.     }

  193.     /**
  194.      * Construct the Malmsten-Blagouchine Fourier Series Term for Log Gamma
  195.      * 
  196.      * @return The Malmsten-Blagouchine Fourier Series Term for Log Gamma
  197.      */

  199.     public static final org.drip.numerical.estimation.R1ToR1SeriesTerm Fourier()
  200.     {
  201.         try
  202.         {
  203.             return new org.drip.numerical.estimation.R1ToR1SeriesTerm()
  204.             {
  205.                 @Override public double value (
  206.                     final int order,
  207.                     final double z)
  208.                     throws java.lang.Exception
  209.                 {
  210.                     if (0 >= order ||
  211.                         !org.drip.numerical.common.NumberUtil.IsValid (z) || 0. >= z || 1. <= z)
  212.                     {
  213.                         throw new java.lang.Exception
  214.                             ("InfiniteSumSeriesTerm::Fourier::value => Invalid Inputs");
  215.                     }

  217.                     return java.lang.Math.log (order) *
  218.                         java.lang.Math.sin (2. * java.lang.Math.PI * order * z) / order;
  219.                 }
  220.             };
  221.         }
  222.         catch (java.lang.Exception e)
  223.         {
  224.             e.printStackTrace();
  225.         }

  227.         return null;
  228.     }

  230.     /**
  231.      * Construct the Blagouchine (2015) Series Term for Log Gamma
  232.      * 
  233.      * @return The Blagouchine (2015) Series Term for Log Gamma
  234.      */

  236.     public static final org.drip.numerical.estimation.R1ToR1SeriesTerm Blagouchine2015()
  237.     {
  238.         try
  239.         {
  240.             return new org.drip.numerical.estimation.R1ToR1SeriesTerm()
  241.             {
  242.                 @Override public double value (
  243.                     final int order,
  244.                     final double z)
  245.                     throws java.lang.Exception
  246.                 {
  247.                     if (0 >= order ||
  248.                         !org.drip.numerical.common.NumberUtil.IsValid (z) || 0. >= z || 1. <= z || 0.5 == z)
  249.                     {
  250.                         throw new java.lang.Exception
  251.                             ("InfiniteSumSeriesTerm::Blagouchine2015::value => Invalid Inputs");
  252.                     }

  254.                     return (
  255.                         org.drip.specialfunction.gamma.Definitions.EULER_MASCHERONI + java.lang.Math.log
  256.                             (order)
  257.                     ) * java.lang.Math.sin (2. * java.lang.Math.PI * order * z) / order;
  258.                 }
  259.             };
  260.         }
  261.         catch (java.lang.Exception e)
  262.         {
  263.             e.printStackTrace();
  264.         }

  266.         return null;
  267.     }
  268. }
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