SphericalSecondEstimator.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>SphericalSecondEstimator</i> implements the Integral Estimator for the Spherical Bessel Function of the
  79.  * Second Kind. 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 SphericalSecondEstimator extends
  116.     org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator
  117. {
  118.     private org.drip.specialfunction.definition.BesselSecondKindEstimator _besselSecondKindEstimator = null;

  120.     /**
  121.      * Retrieve the Order 0 Spherical Bessel Second Kind Estimator
  122.      * 
  123.      * @return The Order 0 Spherical Bessel Second Kind Estimator
  124.      */

  126.     public static final org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator OrderZero()
  127.     {
  128.         return new org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator()
  129.         {
  130.             @Override public double smallY (
  131.                 final double alpha,
  132.                 final double z)
  133.                 throws java.lang.Exception
  134.             {
  135.                 if (0. != alpha ||
  136.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  137.                 {
  138.                     throw new java.lang.Exception
  139.                         ("SphericalFirstEstimator::OrderZero::smallY => Invalid Inputs");
  140.                 }

  142.                 return java.lang.Math.cos (z) / z;
  143.             }
  144.         };
  145.     }

  147.     /**
  148.      * Retrieve the Order +1 Spherical Bessel Second Kind Estimator
  149.      * 
  150.      * @return The Order +1 Spherical Bessel Second Kind Estimator
  151.      */

  153.     public static final org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator OrderPlusOne()
  154.     {
  155.         return new org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator()
  156.         {
  157.             @Override public double smallY (
  158.                 final double alpha,
  159.                 final double z)
  160.                 throws java.lang.Exception
  161.             {
  162.                 if (1. != alpha ||
  163.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  164.                 {
  165.                     throw new java.lang.Exception
  166.                         ("SphericalFirstEstimator::OrderPlusOne::smallY => Invalid Inputs");
  167.                 }

  169.                 double oneOverZ = 1. / z;

  171.                 return -1. * java.lang.Math.cos (z) * oneOverZ * oneOverZ -
  172.                     java.lang.Math.sin (z) * oneOverZ;
  173.             }
  174.         };
  175.     }

  177.     /**
  178.      * Retrieve the Order +2 Spherical Bessel Second Kind Estimator
  179.      * 
  180.      * @return The Order +2 Spherical Bessel Second Kind Estimator
  181.      */

  183.     public static final org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator OrderPlusTwo()
  184.     {
  185.         return new org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator()
  186.         {
  187.             @Override public double smallY (
  188.                 final double alpha,
  189.                 final double z)
  190.                 throws java.lang.Exception
  191.             {
  192.                 if (2. != alpha ||
  193.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  194.                 {
  195.                     throw new java.lang.Exception
  196.                         ("SphericalFirstEstimator::OrderPlusTwo::smallY => Invalid Inputs");
  197.                 }

  199.                 double oneOverZ = 1. / z;
  200.                 double oneOverZ2 = oneOverZ * oneOverZ;

  202.                 return (1. - 3. * oneOverZ2) * java.lang.Math.cos (z) * oneOverZ -
  203.                     3. * java.lang.Math.sin (z) * oneOverZ2;
  204.             }
  205.         };
  206.     }

  208.     /**
  209.      * Retrieve the Order +3 Spherical Bessel Second Kind Estimator
  210.      * 
  211.      * @return The Order +3 Spherical Bessel Second Kind Estimator
  212.      */

  214.     public static final org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator
  215.         OrderPlusThree()
  216.     {
  217.         return new org.drip.specialfunction.definition.SphericalBesselSecondKindEstimator()
  218.         {
  219.             @Override public double smallY (
  220.                 final double alpha,
  221.                 final double z)
  222.                 throws java.lang.Exception
  223.             {
  224.                 if (3. != alpha ||
  225.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  226.                 {
  227.                     throw new java.lang.Exception
  228.                         ("SphericalFirstEstimator::OrderOrderPlusThree::smallY => Invalid Inputs");
  229.                 }

  231.                 double oneOverZ = 1. / z;
  232.                 double oneOverZ2 = oneOverZ * oneOverZ;

  234.                 return (6. * oneOverZ - 15. * oneOverZ2 * oneOverZ) * java.lang.Math.cos (z) * oneOverZ -
  235.                     (15. * oneOverZ2 - 1.) * java.lang.Math.sin (z) * oneOverZ;
  236.             }
  237.         };
  238.     }

  240.     /**
  241.      * SphericalSecondEstimator Constructor
  242.      * 
  243.      * @param besselSecondKindEstimator Bessel Function Second Kind Estimator
  244.      * 
  245.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  246.      */

  248.     public SphericalSecondEstimator (
  249.         final org.drip.specialfunction.definition.BesselSecondKindEstimator besselSecondKindEstimator)
  250.         throws java.lang.Exception
  251.     {
  252.         if (null == (_besselSecondKindEstimator = besselSecondKindEstimator))
  253.         {
  254.             throw new java.lang.Exception ("SphericalSecondEstimator Constructor => Invalid Inputs");
  255.         }
  256.     }

  258.     @Override public double smallY (
  259.         final double alpha,
  260.         final double z)
  261.         throws java.lang.Exception
  262.     {
  263.         return java.lang.Math.sqrt (0.5 * java.lang.Math.PI / z) * _besselSecondKindEstimator.bigY (
  264.             alpha + 0.5,
  265.             z
  266.         );
  267.     }

  269.     /**
  270.      * Retrieve the Bessel Function Second Kind Estimator
  271.      * 
  272.      * @return Bessel Function Second Kind Estimator
  273.      */

  275.     public org.drip.specialfunction.definition.BesselSecondKindEstimator besselSecondKindEstimator()
  276.     {
  277.         return _besselSecondKindEstimator;
  278.     }
  279. }
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