LimitAsymptote.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>LimitAsymptote</i> implements the Asymptotes for the Lower/Upper Incomplete Gamma Function. 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 LimitAsymptote
  119. {

  121.     /**
  122.      * Construct the Lower Incomplete Gamma Asymptote Function
  123.      * 
  124.      * @return The Lower Incomplete Gamma Asymptote Function
  125.      */

  127.     public static final LimitAsymptote Lower()
  128.     {
  129.         return new LimitAsymptote()
  130.         {

  132.             @Override public org.drip.function.definition.R1ToR1 zZero (
  133.                 final double s)
  134.             {
  135.                 if (!org.drip.numerical.common.NumberUtil.IsValid (s))
  136.                 {
  137.                     return null;
  138.                 }

  140.                 return new org.drip.function.definition.R1ToR1 (null)
  141.                 {
  142.                     @Override public double evaluate (
  143.                         final double z)
  144.                         throws java.lang.Exception
  145.                     {
  146.                         if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z < 0.)
  147.                         {
  148.                             throw new java.lang.Exception ("LimitAsymptote::Lower::Zero::evaluate");
  149.                         }

  151.                         return java.lang.Math.pow (
  152.                             z,
  153.                             s
  154.                         ) / s;
  155.                     }
  156.                 };
  157.             }

  159.             @Override public org.drip.function.definition.R1ToR1 zInfinity (
  160.                 final double s)
  161.             {
  162.                 if (!org.drip.numerical.common.NumberUtil.IsValid (s))
  163.                 {
  164.                     return null;
  165.                 }

  167.                 return new org.drip.function.definition.R1ToR1 (null)
  168.                 {
  169.                     @Override public double evaluate (
  170.                         final double z)
  171.                         throws java.lang.Exception
  172.                     {
  173.                         if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z < 0.)
  174.                         {
  175.                             throw new java.lang.Exception ("LimitAsymptote::Lower::Infinity::evaluate");
  176.                         }

  178.                         return new org.drip.specialfunction.gamma.NemesAnalytic (null).evaluate (s);
  179.                     }
  180.                 };
  181.             }
  182.         };
  183.     }

  185.     /**
  186.      * Construct the Upper Incomplete Gamma Asymptote Function
  187.      * 
  188.      * @return The Upper Incomplete Gamma Asymptote Function
  189.      */

  191.     public static final LimitAsymptote Upper()
  192.     {
  193.         return new LimitAsymptote()
  194.         {

  196.             @Override public org.drip.function.definition.R1ToR1 zZero (
  197.                 final double s)
  198.             {
  199.                 return null;
  200.             }

  202.             @Override public org.drip.function.definition.R1ToR1 zInfinity (
  203.                 final double s)
  204.             {
  205.                 if (!org.drip.numerical.common.NumberUtil.IsValid (s))
  206.                 {
  207.                     return null;
  208.                 }

  210.                 return new org.drip.function.definition.R1ToR1 (null)
  211.                 {
  212.                     @Override public double evaluate (
  213.                         final double z)
  214.                         throws java.lang.Exception
  215.                     {
  216.                         if (!org.drip.numerical.common.NumberUtil.IsValid (z) || z < 0.)
  217.                         {
  218.                             throw new java.lang.Exception ("LimitAsymptote::Upper::Infinity::evaluate");
  219.                         }

  221.                         return java.lang.Math.pow (
  222.                             z,
  223.                             s - 1
  224.                         ) * java.lang.Math.exp (-z);
  225.                     }
  226.                 };
  227.             }
  228.         };
  229.     }

  231.     private LimitAsymptote()
  232.     {
  233.     }

  235.     /**
  236.      * Retrieve the z tends to Zero Asymptote
  237.      * 
  238.      * @param s s
  239.      * 
  240.      * @return The z tends to Zero Asymptote
  241.      */

  243.     public abstract org.drip.function.definition.R1ToR1 zZero (
  244.         final double s);

  246.     /**
  247.      * Retrieve the z tends to Infinity Asymptote
  248.      * 
  249.      * @param s s
  250.      * 
  251.      * @return The z tends to Infinity Asymptote
  252.      */

  254.     public abstract org.drip.function.definition.R1ToR1 zInfinity (
  255.         final double s);
  256. }
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