BesselFirstKindEstimator.java

  1. package org.drip.specialfunction.definition;

  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>BesselFirstKindEstimator</i> exposes the Estimator for the Bessel Function of the First Kind. The
  79.  * 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/definition/README.md">Definition of Special Function Estimators</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public abstract class BesselFirstKindEstimator implements org.drip.function.definition.R2ToR1
  116. {

  118.     /**
  119.      * Construct the Alpha Positive Integer or Zero Asymptotic Version of BesselFirstKindEstimator
  120.      * 
  121.      * @param gammaEstimator Gamma Estimator
  122.      * 
  123.      * @return Alpha Positive Integer or Zero Asymptotic Version of BesselFirstKindEstimator
  124.      */

  126.     public static final BesselFirstKindEstimator AlphaPositiveIntegerOrZeroAsymptote (
  127.         final org.drip.function.definition.R1ToR1 gammaEstimator)
  128.     {
  129.         return null == gammaEstimator ? null : new BesselFirstKindEstimator()
  130.         {
  131.             @Override public double bigJ (
  132.                 final double alpha,
  133.                 final double z)
  134.                 throws java.lang.Exception
  135.             {
  136.                 if (!org.drip.numerical.common.NumberUtil.IsInteger (alpha) || 0. > alpha ||
  137.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  138.                 {
  139.                     throw new java.lang.Exception
  140.                         ("BesselFirstKindEstimator::AlphaPositiveIntegerOrZeroAsymptote => Invalid Inputs");
  141.                 }

  143.                 return java.lang.Math.pow (
  144.                     0.5 * z,
  145.                     alpha
  146.                 ) / gammaEstimator.evaluate (alpha + 1.);
  147.             }
  148.         };
  149.     }

  151.     /**
  152.      * Construct the Alpha Negative Integer Asymptotic Version of BesselFirstKindEstimator
  153.      * 
  154.      * @param gammaEstimator Gamma Estimator
  155.      * 
  156.      * @return Alpha Negative Integer Asymptotic Version of BesselFirstKindEstimator
  157.      */

  159.     public static final BesselFirstKindEstimator AlphaNegativeIntegerAsymptote (
  160.         final org.drip.function.definition.R1ToR1 gammaEstimator)
  161.     {
  162.         return null == gammaEstimator ? null : new BesselFirstKindEstimator()
  163.         {
  164.             @Override public double bigJ (
  165.                 final double alpha,
  166.                 final double z)
  167.                 throws java.lang.Exception
  168.             {
  169.                 if (!org.drip.numerical.common.NumberUtil.IsNegativeInteger (alpha) ||
  170.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  171.                 {
  172.                     throw new java.lang.Exception
  173.                         ("BesselFirstKindEstimator::AlphaNegativeIntegerAsymptote => Invalid Inputs");
  174.                 }

  176.                 double negativeAlpha = -1. * alpha;

  178.                 return (0 == negativeAlpha % 2 ? 1. : -1.) * java.lang.Math.pow (
  179.                     0.5 * z,
  180.                     negativeAlpha
  181.                 ) / gammaEstimator.evaluate (negativeAlpha);
  182.             }
  183.         };
  184.     }

  186.     /**
  187.      * Construct the High z Asymptotic Version of BesselFirstKindEstimator
  188.      * 
  189.      * @return High z Asymptotic Version of BesselFirstKindEstimator
  190.      */

  192.     public static final BesselFirstKindEstimator HighZAsymptote()
  193.     {
  194.         return new BesselFirstKindEstimator()
  195.         {
  196.             @Override public double bigJ (
  197.                 final double alpha,
  198.                 final double z)
  199.                 throws java.lang.Exception
  200.             {
  201.                 if (!org.drip.numerical.common.NumberUtil.IsValid (alpha) ||
  202.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  203.                 {
  204.                     throw new java.lang.Exception
  205.                         ("BesselFirstKindEstimator::HighZAsymptote => Invalid Inputs");
  206.                 }

  208.                 return java.lang.Math.sqrt (2. / java.lang.Math.PI / z) * java.lang.Math.cos (
  209.                     z - 0.5 * java.lang.Math.PI * alpha - 0.25 * java.lang.Math.PI
  210.                 );
  211.             }
  212.         };
  213.     }

  215.     /**
  216.      * Construct the Alpha=0 Negative z Asymptotic Version of BesselFirstKindEstimator
  217.      * 
  218.      * @return Alpha=0 Negative z Asymptotic Version of BesselFirstKindEstimator
  219.      */

  221.     public static final BesselFirstKindEstimator AlphaZeroNegativeZAsymptote()
  222.     {
  223.         return new BesselFirstKindEstimator()
  224.         {
  225.             @Override public double bigJ (
  226.                 final double alpha,
  227.                 final double z)
  228.                 throws java.lang.Exception
  229.             {
  230.                 if (0. != alpha ||
  231.                     !org.drip.numerical.common.NumberUtil.IsValid (z) || 0. < z)
  232.                 {
  233.                     throw new java.lang.Exception
  234.                         ("BesselFirstKindEstimator::AlphaZeroNegativeZAsymptote => Invalid Inputs");
  235.                 }

  237.                 return java.lang.Math.sqrt (-2. / java.lang.Math.PI / z) * java.lang.Math.cos (
  238.                     z + 0.25 * java.lang.Math.PI
  239.                 );
  240.             }
  241.         };
  242.     }

  244.     public static final BesselFirstKindEstimator AlphaZeroApproximate()
  245.     {
  246.         return new BesselFirstKindEstimator()
  247.         {
  248.             @Override public double bigJ (
  249.                 final double alpha,
  250.                 final double z)
  251.                 throws java.lang.Exception
  252.             {
  253.                 if (0. != alpha ||
  254.                     !org.drip.numerical.common.NumberUtil.IsValid (z))
  255.                 {
  256.                     throw new java.lang.Exception
  257.                         ("BesselFirstKindEstimator::AlphaZeroApproximate => Invalid Inputs");
  258.                 }

  260.                 double oneOver_OnePlus__zOver7_Power20__ = 1. / (
  261.                     1 + java.lang.Math.pow (
  262.                         z / 7.,
  263.                         20.
  264.                     )
  265.                 );

  267.                 double zAbsolute = java.lang.Math.abs (z);

  269.                 double zOver2 = z / 2.;
  270.                 double zSign = 0 == z ? 1. : zAbsolute / z;

  272.                 return oneOver_OnePlus__zOver7_Power20__ * (
  273.                     (1. + java.lang.Math.cos (z)) / 6. + (
  274.                         java.lang.Math.cos (zOver2) + java.lang.Math.cos (java.lang.Math.sqrt (3.) * zOver2)
  275.                     ) / 3.
  276.                 ) +
  277.                 (1. - oneOver_OnePlus__zOver7_Power20__) * java.lang.Math.sqrt (
  278.                     2. / java.lang.Math.PI / zAbsolute
  279.                 ) * java.lang.Math.cos (
  280.                     z -  0.25 * java.lang.Math.PI * zSign
  281.                 );
  282.             }
  283.         };
  284.     }

  286.     /**
  287.      * Evaluate Bessel Function First Kind J given Alpha and z
  288.      * 
  289.      * @param alpha Alpha
  290.      * @param z Z
  291.      *  
  292.      * @return Bessel Function First Kind J Value
  293.      * 
  294.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  295.      */

  297.     public abstract double bigJ (
  298.         final double alpha,
  299.         final double z)
  300.         throws java.lang.Exception;

  302.     @Override public double evaluate (
  303.         final double alpha,
  304.         final double z)
  305.         throws java.lang.Exception
  306.     {
  307.         return bigJ (
  308.             alpha,
  309.             z
  310.         );
  311.     }
  312. }
Created with JaCoCo 0.7.9.201702052155