LowerSFixedSeries.java

  1. package org.drip.specialfunction.incompletegamma;

  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>LowerSFixedSeries</i> implements Lower Incomplete Gamma Expansion Series. The References are:
  79.  * 
  80.  * <br><br>
  81.  *  <ul>
  82.  *      <li>
  83.  *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
  84.  *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
  85.  *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
  86.  *      </li>
  87.  *      <li>
  88.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  89.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
  93.  *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
  94.  *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions
  98.  *              https://dlmf.nist.gov/8
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2019): Incomplete Gamma Function
  102.  *              https://en.wikipedia.org/wiki/Incomplete_gamma_function
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  110.  *      <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>
  111.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/gammaincomplete/README.md">Upper/Lower Incomplete Gamma Functions</a></li>
  112.  *  </ul>
  113.  *
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public class LowerSFixedSeries extends org.drip.numerical.estimation.R1ToR1Series
  118. {
  119.     private double _s = java.lang.Double.NaN;
  120.     private double _logGammaS = java.lang.Double.NaN;

  122.     /**
  123.      * Construct the R<sup>1</sup> To R<sup>1</sup> Weierstrass Limit Series
  124.      * 
  125.      * @param s Incomplete Gamma s
  126.      * @param termCount Count of the Number of Terms
  127.      * 
  128.      * @return The R<sup>1</sup> To R<sup>1</sup> Weierstrass Limit Series
  129.      */

  131.     public static final LowerSFixedSeries WeierstrassLimit (
  132.         final double s,
  133.         final int termCount)
  134.     {
  135.         java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  136.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  138.         for (int termIndex = 0; termIndex <= termCount; ++termIndex)
  139.         {
  140.             termWeightMap.put (
  141.                 termIndex,
  142.                 1.
  143.             );
  144.         }

  146.         try
  147.         {
  148.             return new LowerSFixedSeries (
  149.                 org.drip.specialfunction.incompletegamma.LowerSFixedSeriesTerm.WeierstrassLimit (s),
  150.                 termWeightMap,
  151.                 s,
  152.                 0 == s ? 1. : new org.drip.specialfunction.loggamma.NemesAnalyticEstimator (null).evaluate (s)
  153.             );
  154.         }
  155.         catch (java.lang.Exception e)
  156.         {
  157.             e.printStackTrace();
  158.         }

  160.         return null;
  161.     }

  163.     /**
  164.      * Construct the R<sup>1</sup> To R<sup>1</sup> NIST (2019) Limit Series
  165.      * 
  166.      * @param s Incomplete Gamma s
  167.      * @param termCount Count of the Number of Terms
  168.      * 
  169.      * @return The R<sup>1</sup> To R<sup>1</sup> NIST (2019) Limit Series
  170.      */

  172.     public static final LowerSFixedSeries NIST2019 (
  173.         final double s,
  174.         final int termCount)
  175.     {
  176.         try
  177.         {
  178.             double logGammaS = new org.drip.specialfunction.loggamma.NemesAnalyticEstimator (null).evaluate (s);

  180.             java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
  181.                 java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  183.             for (int termIndex = 0; termIndex <= termCount; ++termIndex)
  184.             {
  185.                 termWeightMap.put (
  186.                     termIndex,
  187.                     1.
  188.                 );
  189.             }

  191.             return new LowerSFixedSeries (
  192.                 org.drip.specialfunction.incompletegamma.LowerSFixedSeriesTerm.NIST2019 (
  193.                     s,
  194.                     logGammaS
  195.                 ),
  196.                 termWeightMap,
  197.                 s,
  198.                 logGammaS
  199.             );
  200.         }
  201.         catch (java.lang.Exception e)
  202.         {
  203.             e.printStackTrace();
  204.         }

  206.         return null;
  207.     }

  209.     /**
  210.      * LowerSFixedSeries Constructor
  211.      * 
  212.      * @param r1ToR1SeriesTerm R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
  213.      * @param termWeightMap Error Term Weight Map
  214.      * @param s s
  215.      * @param logGammaS Log (Gamma (s))
  216.      * 
  217.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  218.      */

  220.     public LowerSFixedSeries (
  221.         final org.drip.numerical.estimation.R1ToR1SeriesTerm r1ToR1SeriesTerm,
  222.         final java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap,
  223.         final double s,
  224.         final double logGammaS)
  225.         throws java.lang.Exception
  226.     {
  227.         super (
  228.             r1ToR1SeriesTerm,
  229.             false,
  230.             termWeightMap
  231.         );

  233.         if (!org.drip.numerical.common.NumberUtil.IsValid (_s = s) ||
  234.             !org.drip.numerical.common.NumberUtil.IsValid (_logGammaS = logGammaS))
  235.         {
  236.             throw new java.lang.Exception ("LowerSFixedSeries Constructor => Invalid Inputs");
  237.         }
  238.     }

  240.     /**
  241.      * Retrieve s
  242.      * 
  243.      * @return s
  244.      */

  246.     public double s()
  247.     {
  248.         return _s;
  249.     }

  251.     /**
  252.      * Retrieve Log (Gamma (s))
  253.      * 
  254.      * @return Log (Gamma (s))
  255.      */

  257.     public double logGammaS()
  258.     {
  259.         return _logGammaS;
  260.     }
  261. }
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