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<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml" lang="en"><head><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"/><link rel="stylesheet" href="../jacoco-resources/report.css" type="text/css"/><link rel="shortcut icon" href="../jacoco-resources/report.gif" type="image/gif"/><title>SecondNISTSeriesTerm.java</title><link rel="stylesheet" href="../jacoco-resources/prettify.css" type="text/css"/><script type="text/javascript" src="../jacoco-resources/prettify.js"></script></head><body onload="window['PR_TAB_WIDTH']=4;prettyPrint()"><div class="breadcrumb" id="breadcrumb"><span class="info"><a href="../jacoco-sessions.html" class="el_session">Sessions</a></span><a href="../index.html" class="el_report">DROP</a> > <a href="index.source.html" class="el_package">org.drip.specialfunction.bessel</a> > <span class="el_source">SecondNISTSeriesTerm.java</span></div><h1>SecondNISTSeriesTerm.java</h1><pre class="source lang-java linenums">
package org.drip.specialfunction.bessel;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>SecondNISTSeriesTerm</i> implements the Series Term for the Cylindrical Bessel Function of the Second
* Kind using the NIST Series. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
* on Mathematics</b>
* </li>
* <li>
* Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
* Edition</i> <b>Harcourt</b> San Diego
* </li>
* <li>
* Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
* Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
* </li>
* <li>
* Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
* Press</b>
* </li>
* <li>
* Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class SecondNISTSeriesTerm extends org.drip.numerical.estimation.R2ToR1SeriesTerm
{
<span class="nc" id="L118"> private org.drip.function.definition.R1ToR1 _gammaEstimator = null;</span>
<span class="nc" id="L119"> private org.drip.function.definition.R1ToR1 _digammaEstimator = null;</span>
/**
* SecondNISTSeriesTerm Constructor
*
* @param digammaEstimator Digamma Function Estimator
* @param gammaEstimator Gamma Estimator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public SecondNISTSeriesTerm (
final org.drip.function.definition.R1ToR1 digammaEstimator,
final org.drip.function.definition.R1ToR1 gammaEstimator)
throws java.lang.Exception
<span class="nc" id="L134"> {</span>
<span class="nc bnc" id="L135" title="All 4 branches missed."> if (null == (_digammaEstimator = digammaEstimator) ||</span>
null == (_gammaEstimator = gammaEstimator))
{
<span class="nc" id="L138"> throw new java.lang.Exception ("SecondNISTSeriesTerm Constructor => Invalid Input");</span>
}
<span class="nc" id="L140"> }</span>
/**
* Retrieve the Digamma Function Estimator
*
* @return The Digamma Function Estimator
*/
public org.drip.function.definition.R1ToR1 digammaEstimator()
{
<span class="nc" id="L150"> return _digammaEstimator;</span>
}
/**
* Retrieve the Gamma Estimator
*
* @return The Gamma Estimator
*/
public org.drip.function.definition.R1ToR1 gammaEstimator()
{
<span class="nc" id="L161"> return _gammaEstimator;</span>
}
@Override public double value (
final int order,
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L170" title="All 2 branches missed."> if (0 > order ||</span>
<span class="nc bnc" id="L171" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (alpha) ||</span>
<span class="nc bnc" id="L172" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L174"> throw new java.lang.Exception ("SecondNISTSeriesTerm::value => Invalid Inputs");</span>
}
<span class="nc" id="L177"> double oneOverPI = 1. / java.lang.Math.PI;</span>
<span class="nc" id="L179"> double _zOver2_PowerAlpha = java.lang.Math.pow (</span>
0.5 * z,
alpha
);
<span class="nc" id="L184"> double _zSquaredOver4_PowerOrder = java.lang.Math.pow (</span>
0.25 * z * z,
order
);
<span class="nc bnc" id="L189" title="All 2 branches missed."> double bigY = (</span>
0 == order % 2 ? -1. : 1.
) * _zOver2_PowerAlpha * oneOverPI * (
<span class="nc" id="L192"> _digammaEstimator.evaluate (order + 1) +</span>
<span class="nc" id="L193"> _digammaEstimator.evaluate (alpha + order + 1)</span>
) * _zSquaredOver4_PowerOrder / (
<span class="nc" id="L195"> _gammaEstimator.evaluate (order + 1) *</span>
<span class="nc" id="L196"> _gammaEstimator.evaluate (alpha + order + 1)</span>
);
<span class="nc bnc" id="L199" title="All 2 branches missed."> if (order < alpha)</span>
{
<span class="nc" id="L201"> bigY = bigY - 1. / _zOver2_PowerAlpha * oneOverPI * _gammaEstimator.evaluate (alpha - order) /</span>
<span class="nc" id="L202"> _gammaEstimator.evaluate (order + 1) * _zSquaredOver4_PowerOrder;</span>
}
<span class="nc" id="L205"> return bigY;</span>
}
}
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