SecondNISTSeriesTerm.java

  1. package org.drip.specialfunction.bessel;

  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>SecondNISTSeriesTerm</i> implements the Series Term for the Cylindrical Bessel Function of the Second
  79.  * Kind using the NIST Series. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  85.  *              on Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
  89.  *              Edition</i> <b>Harcourt</b> San Diego
  90.  *      </li>
  91.  *      <li>
  92.  *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
  93.  *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
  94.  *      </li>
  95.  *      <li>
  96.  *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
  97.  *              Press</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_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/bessel/README.md">Ordered Bessel Function Variant Estimators</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class SecondNISTSeriesTerm extends org.drip.numerical.estimation.R2ToR1SeriesTerm
  116. {
  117.     private org.drip.function.definition.R1ToR1 _gammaEstimator = null;
  118.     private org.drip.function.definition.R1ToR1 _digammaEstimator = null;

  120.     /**
  121.      * SecondNISTSeriesTerm Constructor
  122.      * 
  123.      * @param digammaEstimator Digamma Function Estimator
  124.      * @param gammaEstimator Gamma Estimator
  125.      * 
  126.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  127.      */

  129.     public SecondNISTSeriesTerm (
  130.         final org.drip.function.definition.R1ToR1 digammaEstimator,
  131.         final org.drip.function.definition.R1ToR1 gammaEstimator)
  132.         throws java.lang.Exception
  133.     {
  134.         if (null == (_digammaEstimator = digammaEstimator) ||
  135.             null == (_gammaEstimator = gammaEstimator))
  136.         {
  137.             throw new java.lang.Exception ("SecondNISTSeriesTerm Constructor => Invalid Input");
  138.         }
  139.     }

  141.     /**
  142.      * Retrieve the Digamma Function Estimator
  143.      * 
  144.      * @return The Digamma Function Estimator
  145.      */

  147.     public org.drip.function.definition.R1ToR1 digammaEstimator()
  148.     {
  149.         return _digammaEstimator;
  150.     }

  152.     /**
  153.      * Retrieve the Gamma Estimator
  154.      * 
  155.      * @return The Gamma Estimator
  156.      */

  158.     public org.drip.function.definition.R1ToR1 gammaEstimator()
  159.     {
  160.         return _gammaEstimator;
  161.     }

  163.     @Override public double value (
  164.         final int order,
  165.         final double alpha,
  166.         final double z)
  167.         throws java.lang.Exception
  168.     {
  169.         if (0 > order ||
  170.             !org.drip.numerical.common.NumberUtil.IsValid (alpha) ||
  171.             !org.drip.numerical.common.NumberUtil.IsValid (z))
  172.         {
  173.             throw new java.lang.Exception ("SecondNISTSeriesTerm::value => Invalid Inputs");
  174.         }

  176.         double oneOverPI = 1. / java.lang.Math.PI;

  178.         double _zOver2_PowerAlpha = java.lang.Math.pow (
  179.             0.5 * z,
  180.             alpha
  181.         );

  183.         double _zSquaredOver4_PowerOrder = java.lang.Math.pow (
  184.             0.25 * z * z,
  185.             order
  186.         );

  188.         double bigY = (
  189.             0 == order % 2 ? -1. : 1.
  190.         ) * _zOver2_PowerAlpha * oneOverPI * (
  191.             _digammaEstimator.evaluate (order + 1) +
  192.             _digammaEstimator.evaluate (alpha + order + 1)
  193.         ) * _zSquaredOver4_PowerOrder / (
  194.             _gammaEstimator.evaluate (order + 1) *
  195.             _gammaEstimator.evaluate (alpha + order + 1)
  196.         );

  198.         if (order < alpha)
  199.         {
  200.             bigY = bigY - 1. / _zOver2_PowerAlpha * oneOverPI * _gammaEstimator.evaluate (alpha - order) /
  201.                 _gammaEstimator.evaluate (order + 1) * _zSquaredOver4_PowerOrder;
  202.         }

  204.         return bigY;
  205.     }
  206. }
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