LowerSFixed.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>LowerSFixed</i> implements the Lower Incomplete Gamma Function using Power Series for a Fixed s. The
  79.  * References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
  85.  *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
  86.  *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
  87.  *      </li>
  88.  *      <li>
  89.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  90.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
  94.  *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
  95.  *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
  96.  *      </li>
  97.  *      <li>
  98.  *          National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions
  99.  *              https://dlmf.nist.gov/8
  100.  *      </li>
  101.  *      <li>
  102.  *          Wikipedia (2019): Incomplete Gamma Function
  103.  *              https://en.wikipedia.org/wiki/Incomplete_gamma_function
  104.  *      </li>
  105.  *  </ul>
  106.  *
  107.  *  <br><br>
  108.  *  <ul>
  109.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  110.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  111.  *      <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>
  112.  *      <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>
  113.  *  </ul>
  114.  *
  115.  * @author Lakshmi Krishnamurthy
  116.  */

  118. public abstract class LowerSFixed extends org.drip.numerical.estimation.R1ToR1Estimator
  119. {
  120.     private org.drip.specialfunction.incompletegamma.LowerSFixedSeries _lowerSFixedSeries = null;

  122.     /**
  123.      * Construct the Weierstrass Lower S Fixed Series Incomplete Gamma Estimator
  124.      * 
  125.      * @param s Incomplete Gamma s
  126.      * @param termCount Count of the Number of Terms
  127.      * 
  128.      * @return The Weierstrass Lower S Fixed Series Incomplete Gamma Estimator
  129.      */

  131.     public static final LowerSFixed WeierstrassLimit (
  132.         final double s,
  133.         final int termCount)
  134.     {
  135.         try
  136.         {
  137.             return new LowerSFixed (
  138.                 org.drip.specialfunction.incompletegamma.LowerSFixedSeries.WeierstrassLimit (
  139.                     s,
  140.                     termCount
  141.                 ),
  142.                 null
  143.             )
  144.             {
  145.                 @Override public double nonDimensional (
  146.                     final double z)
  147.                     throws java.lang.Exception
  148.                 {
  149.                     return weierstrassLimit (z) * java.lang.Math.exp (-1. * z);
  150.                 }
  151.             };
  152.         }
  153.         catch (java.lang.Exception e)
  154.         {
  155.             e.printStackTrace();
  156.         }

  158.         return null;
  159.     }

  161.     /**
  162.      * Construct the NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator
  163.      * 
  164.      * @param s Incomplete Gamma s
  165.      * @param termCount Count of the Number of Terms
  166.      * 
  167.      * @return The NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator
  168.      */

  170.     public static final LowerSFixed NIST2019 (
  171.         final double s,
  172.         final int termCount)
  173.     {
  174.         try
  175.         {
  176.             return new LowerSFixed (
  177.                 org.drip.specialfunction.incompletegamma.LowerSFixedSeries.NIST2019 (
  178.                     s,
  179.                     termCount
  180.                 ),
  181.                 null
  182.             )
  183.             {
  184.                 @Override public double nonDimensional (
  185.                     final double z)
  186.                     throws java.lang.Exception
  187.                 {
  188.                     return weierstrassLimit (z);
  189.                 }
  190.             };
  191.         }
  192.         catch (java.lang.Exception e)
  193.         {
  194.             e.printStackTrace();
  195.         }

  197.         return null;
  198.     }

  200.     /**
  201.      * LowerSFixed Constructor
  202.      * 
  203.      * @param lowerSFixedSeries R<sup>1</sup> To R<sup>1</sup> Lower S Fixed Limit Series
  204.      * @param dc Differential Control
  205.      * 
  206.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  207.      */

  209.     public LowerSFixed (
  210.         final org.drip.specialfunction.incompletegamma.LowerSFixedSeries lowerSFixedSeries,
  211.         final org.drip.numerical.differentiation.DerivativeControl dc)
  212.         throws java.lang.Exception
  213.     {
  214.         super (dc);

  216.         _lowerSFixedSeries = lowerSFixedSeries;
  217.     }

  219.     @Override public org.drip.numerical.estimation.R1Estimate seriesEstimateNative (
  220.         final double x)
  221.     {
  222.         return null == _lowerSFixedSeries ? seriesEstimate (
  223.             x,
  224.             null,
  225.             null
  226.         ) : seriesEstimate (
  227.             x,
  228.             _lowerSFixedSeries.termWeightMap(),
  229.             _lowerSFixedSeries
  230.         );
  231.     }

  233.     /**
  234.      * Compute the Limiting Weierstrass Sum
  235.      * 
  236.      * @param z Z
  237.      * 
  238.      * @return The Limiting Weierstrass Sum
  239.      * 
  240.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  241.      */

  243.     public double weierstrassLimit (
  244.         final double z)
  245.         throws java.lang.Exception
  246.     {
  247.         return _lowerSFixedSeries.evaluate (z);
  248.     }

  250.     /**
  251.      * Compute the Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)
  252.      * 
  253.      * @param z Z
  254.      * 
  255.      * @return The Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)
  256.      * 
  257.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  258.      */

  260.     public abstract double nonDimensional (
  261.         final double z)
  262.         throws java.lang.Exception;

  264.     @Override public double evaluate (
  265.         final double z)
  266.         throws java.lang.Exception
  267.     {
  268.         return java.lang.Math.exp (
  269.             _lowerSFixedSeries.s() * java.lang.Math.log (z) + _lowerSFixedSeries.logGammaS()
  270.         ) * nonDimensional (z);
  271.     }
  272. }
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