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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>SphericalFirstEstimator.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">SphericalFirstEstimator.java</span></div><h1>SphericalFirstEstimator.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>SphericalFirstEstimator</i> implements the Integral Estimator for the Spherical Bessel Function of the
* First Kind. 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 SphericalFirstEstimator extends
org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
{
<span class="nc" id="L119"> private org.drip.specialfunction.definition.BesselFirstKindEstimator _besselFirstKindEstimator = null;</span>
/**
* Retrieve the Order 0 Spherical Bessel First Kind Estimator
*
* @return The Order 0 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderZero()
{
<span class="nc" id="L129"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L130"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L136" title="All 2 branches missed."> if (0. != alpha ||</span>
<span class="nc bnc" id="L137" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L139"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderZero::smallJ => Invalid Inputs");
}
<span class="nc bnc" id="L143" title="All 2 branches missed."> return 0. == z ? 1. : java.lang.Math.sin (z) / z;</span>
}
};
}
/**
* Retrieve the Order +1 Spherical Bessel First Kind Estimator
*
* @return The Order +1 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderPlusOne()
{
<span class="nc" id="L156"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L157"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L163" title="All 2 branches missed."> if (1. != alpha ||</span>
<span class="nc bnc" id="L164" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L166"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderPlusOne::smallJ => Invalid Inputs");
}
<span class="nc" id="L170"> return java.lang.Math.sin (z) / (z * z) - java.lang.Math.cos (z) / z;</span>
}
};
}
/**
* Retrieve the Order -1 Spherical Bessel First Kind Estimator
*
* @return The Order -1 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderMinusOne()
{
<span class="nc" id="L183"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L184"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L190" title="All 2 branches missed."> if (-1. != alpha ||</span>
<span class="nc bnc" id="L191" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L193"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderMinusOne::smallJ => Invalid Inputs");
}
<span class="nc" id="L197"> return java.lang.Math.cos (z) / z;</span>
}
};
}
/**
* Retrieve the Order +2 Spherical Bessel First Kind Estimator
*
* @return The Order +2 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderPlusTwo()
{
<span class="nc" id="L210"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L211"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L217" title="All 2 branches missed."> if (2. != alpha ||</span>
<span class="nc bnc" id="L218" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L220"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderPlusTwo::smallJ => Invalid Inputs");
}
<span class="nc" id="L224"> double oneOverZ = 1. / z;</span>
<span class="nc" id="L225"> double oneOverZ2 = oneOverZ * oneOverZ;</span>
<span class="nc" id="L227"> return (3. * oneOverZ2 - 1.) * java.lang.Math.sin (z) * oneOverZ -</span>
<span class="nc" id="L228"> 3. * java.lang.Math.cos (z) * oneOverZ2;</span>
}
};
}
/**
* Retrieve the Order -2 Spherical Bessel First Kind Estimator
*
* @return The Order -2 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator OrderMinusTwo()
{
<span class="nc" id="L241"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L242"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L248" title="All 2 branches missed."> if (-2. != alpha ||</span>
<span class="nc bnc" id="L249" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L251"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderMinusTwo::smallJ => Invalid Inputs");
}
<span class="nc" id="L255"> double oneOverZ = 1. / z;</span>
<span class="nc" id="L257"> return -1. * java.lang.Math.cos (z) * oneOverZ * oneOverZ -</span>
<span class="nc" id="L258"> java.lang.Math.sin (z) * oneOverZ;</span>
}
};
}
/**
* Retrieve the Order +3 Spherical Bessel First Kind Estimator
*
* @return The Order +3 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
OrderPlusThree()
{
<span class="nc" id="L272"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L273"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L279" title="All 2 branches missed."> if (3. != alpha ||</span>
<span class="nc bnc" id="L280" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L282"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderPlusThree::smallJ => Invalid Inputs");
}
<span class="nc" id="L286"> double oneOverZ = 1. / z;</span>
<span class="nc" id="L287"> double oneOverZ2 = oneOverZ * oneOverZ;</span>
<span class="nc" id="L289"> return (15. * oneOverZ2 * oneOverZ - 6. * oneOverZ) * java.lang.Math.sin (z) * oneOverZ -</span>
<span class="nc" id="L290"> (15. * oneOverZ2 - 1.) * java.lang.Math.cos (z) * oneOverZ;</span>
}
};
}
/**
* Retrieve the Order -3 Spherical Bessel First Kind Estimator
*
* @return The Order -3 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
OrderMinusThree()
{
<span class="nc" id="L304"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L305"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L311" title="All 2 branches missed."> if (-3. != alpha ||</span>
<span class="nc bnc" id="L312" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L314"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderMinusThree::smallJ => Invalid Inputs");
}
<span class="nc" id="L318"> double oneOverZ = 1. / z;</span>
<span class="nc" id="L319"> double oneOverZ2 = oneOverZ * oneOverZ;</span>
<span class="nc" id="L321"> return (1. - 3. * oneOverZ2) * java.lang.Math.cos (z) * oneOverZ -</span>
<span class="nc" id="L322"> 3. * java.lang.Math.sin (z) * oneOverZ2;</span>
}
};
}
/**
* Retrieve the Order -4 Spherical Bessel First Kind Estimator
*
* @return The Order -4 Spherical Bessel First Kind Estimator
*/
public static final org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator
OrderMinusFour()
{
<span class="nc" id="L336"> return new org.drip.specialfunction.definition.SphericalBesselFirstKindEstimator()</span>
<span class="nc" id="L337"> {</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc bnc" id="L343" title="All 2 branches missed."> if (-4. != alpha ||</span>
<span class="nc bnc" id="L344" title="All 2 branches missed."> !org.drip.numerical.common.NumberUtil.IsValid (z))</span>
{
<span class="nc" id="L346"> throw new java.lang.Exception</span>
("SphericalFirstEstimator::OrderOrderMinusFour::smallJ => Invalid Inputs");
}
<span class="nc" id="L350"> double oneOverZ = 1. / z;</span>
<span class="nc" id="L351"> double oneOverZ2 = oneOverZ * oneOverZ;</span>
<span class="nc" id="L353"> return (6. * oneOverZ - 15. * oneOverZ2 * oneOverZ) * java.lang.Math.cos (z) * oneOverZ -</span>
<span class="nc" id="L354"> (15. * oneOverZ2 - 1.) * java.lang.Math.sin (z) * oneOverZ;</span>
}
};
}
/**
* SphericalFirstEstimator Constructor
*
* @param besselFirstKindEstimator Bessel Function First Kind Estimator
*
* @throws java.lang.Exception Thrown if Inputs are Invalid
*/
public SphericalFirstEstimator (
final org.drip.specialfunction.definition.BesselFirstKindEstimator besselFirstKindEstimator)
throws java.lang.Exception
<span class="nc" id="L370"> {</span>
<span class="nc bnc" id="L371" title="All 2 branches missed."> if (null == (_besselFirstKindEstimator = besselFirstKindEstimator))</span>
{
<span class="nc" id="L373"> throw new java.lang.Exception ("SphericalFirstEstimator Constructor => Invalid Inputs");</span>
}
<span class="nc" id="L375"> }</span>
@Override public double smallJ (
final double alpha,
final double z)
throws java.lang.Exception
{
<span class="nc" id="L382"> return java.lang.Math.sqrt (0.5 * java.lang.Math.PI / z) * _besselFirstKindEstimator.bigJ (</span>
alpha + 0.5,
z
);
}
/**
* Retrieve the Bessel Function First Kind Estimator
*
* @return Bessel Function First Kind Estimator
*/
public org.drip.specialfunction.definition.BesselFirstKindEstimator besselFirstKindEstimator()
{
<span class="nc" id="L396"> return _besselFirstKindEstimator;</span>
}
}
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