RaabeSeriesEstimator.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>RaabeSeriesEstimator</i> implements the Raabe Series Version of Log Gamma Function. This Version is
  79.  * Series Convergent. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function <i>Computers and
  85.  *              Mathematics with Applications</i> <b>61 (11)</b> 3364-3369
  86.  *      </li>
  87.  *      <li>
  88.  *          National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical
  89.  *              Functions https://dlmf.nist.gov/5.11
  90.  *      </li>
  91.  *      <li>
  92.  *          Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n!
  93.  *              https://arxiv.org/abs/1003.2907 <b>arXiv</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Toth V. T. (2016): Programmable Calculators – The Gamma Function
  97.  *              http://www.rskey.org/CMS/index.php/the-library/11
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Stirling's Approximation
  101.  *              https://en.wikipedia.org/wiki/Stirling%27s_approximation
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  109.  *      <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>
  110.  *      <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>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class RaabeSeriesEstimator extends org.drip.numerical.estimation.R1ToR1Estimator
  117. {

  119.     /**
  120.      * RaabeSeriesEstimator Constructor
  121.      * 
  122.      * @param dc The Derivative Control
  123.      */

  125.     public RaabeSeriesEstimator (
  126.         final org.drip.numerical.differentiation.DerivativeControl dc)
  127.     {
  128.         super (dc);
  129.     }

  131.     @Override public double evaluate (
  132.         final double x)
  133.         throws java.lang.Exception
  134.     {
  135.         if (!org.drip.numerical.common.NumberUtil.IsValid (x) || 0. >= x)
  136.         {
  137.             throw new java.lang.Exception ("RaabeSeriesEstimator::evaluate => Invalid Inputs");
  138.         }

  140.         return x * java.lang.Math.log (x) - x + 0.5 * java.lang.Math.log (2. * java.lang.Math.PI / x);
  141.     }

  143.     /**
  144.      * Compute the Bounded Function Estimates along with the Higher Order Inverted Rising Exponentials
  145.      * 
  146.      * @param x X
  147.      * 
  148.      * @return The Bounded Function Estimates along with the Higher Order Inverted Rising Exponentials
  149.      */

  151.     public org.drip.numerical.estimation.R1Estimate invertedRisingExponentialCorrectionEstimate (
  152.         final double x)
  153.     {
  154.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  155.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  157.         termWeightMap.put (
  158.             1,
  159.             1. / 12.
  160.         );

  162.         termWeightMap.put (
  163.             2,
  164.             1. / 12.
  165.         );

  167.         termWeightMap.put (
  168.             3,
  169.             59. / 360.
  170.         );

  172.         termWeightMap.put (
  173.             4,
  174.             29. / 60.
  175.         );

  177.         try
  178.         {
  179.             return seriesEstimate (
  180.                 x,
  181.                 termWeightMap,
  182.                 new org.drip.numerical.estimation.R1ToR1Series (
  183.                     org.drip.numerical.estimation.R1ToR1SeriesTerm.InvertedRisingExponential(),
  184.                     false,
  185.                     termWeightMap
  186.                 )
  187.             );
  188.         }
  189.         catch (java.lang.Exception e)
  190.         {
  191.             e.printStackTrace();
  192.         }

  194.         return null;
  195.     }

  197.     /**
  198.      * Compute the Raabe's Strip Integral between (a, a + 1) for the Log Gamma Function
  199.      * 
  200.      * @param a a
  201.      * 
  202.      * @return The Raabe's Strip Integral between (a, a + 1) for the Log Gamma Function
  203.      * 
  204.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  205.      */

  207.     public double stripIntegral (
  208.         final double a)
  209.         throws java.lang.Exception
  210.     {
  211.         if (!org.drip.numerical.common.NumberUtil.IsValid (a) || 0. > a)
  212.         {
  213.             throw new java.lang.Exception ("RaabeSeriesEstimator::stripIntegral => Invalid Inputs");
  214.         }

  216.         return 0.5 * java.lang.Math.log (2. * java.lang.Math.PI) + a * java.lang.Math.log (a) - a;
  217.     }
  218. }
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