jacoco/org.drip.specialfunction.bessel/SecondWatsonIntegralEstimator.java.html

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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                     =&gt; https://lakshmidrip.github.io/DROP/
 * 	- Wiki                     =&gt; https://github.com/lakshmiDRIP/DROP/wiki
 * 	- GitHub                   =&gt; https://github.com/lakshmiDRIP/DROP
 * 	- Repo Layout Taxonomy     =&gt; https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 * 	- Javadoc                  =&gt; https://lakshmidrip.github.io/DROP/Javadoc/index.html
 * 	- Technical Specifications =&gt; https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 * 	- Release Versions         =&gt; https://lakshmidrip.github.io/DROP/version.html
 * 	- Community Credits        =&gt; https://lakshmidrip.github.io/DROP/credits.html
 * 	- Issues Catalog           =&gt; https://github.com/lakshmiDRIP/DROP/issues
 * 	- JUnit                    =&gt; https://lakshmidrip.github.io/DROP/junit/index.html
 * 	- Jacoco                   =&gt; https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);
 *   	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 &quot;AS IS&quot; 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.
 */

/**
 * &lt;i&gt;SecondWatsonIntegralEstimator&lt;/i&gt; implements the Integral Estimator for the Cylindrical Bessel Function
 * of the Second Kind. The References are:
 * 
 * &lt;br&gt;&lt;br&gt;
 * 	&lt;ul&gt;
 * 		&lt;li&gt;
 * 			Abramowitz, M., and I. A. Stegun (2007): &lt;i&gt;Handbook of Mathematics Functions&lt;/i&gt; &lt;b&gt;Dover Book
 * 				on Mathematics&lt;/b&gt;
 * 		&lt;/li&gt;
 * 		&lt;li&gt;
 * 			Arfken, G. B., and H. J. Weber (2005): &lt;i&gt;Mathematical Methods for Physicists 6&lt;sup&gt;th&lt;/sup&gt;
 * 				Edition&lt;/i&gt; &lt;b&gt;Harcourt&lt;/b&gt; San Diego
 * 		&lt;/li&gt;
 * 		&lt;li&gt;
 * 			Temme N. M. (1996): &lt;i&gt;Special Functions: An Introduction to the Classical Functions of
 * 				Mathematical Physics 2&lt;sup&gt;nd&lt;/sup&gt; Edition&lt;/i&gt; &lt;b&gt;Wiley&lt;/b&gt; New York
 * 		&lt;/li&gt;
 * 		&lt;li&gt;
 * 			Watson, G. N. (1995): &lt;i&gt;A Treatise on the Theory of Bessel Functions&lt;/i&gt; &lt;b&gt;Cambridge University
 * 				Press&lt;/b&gt;
 * 		&lt;/li&gt;
 * 		&lt;li&gt;
 * 			Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
 * 		&lt;/li&gt;
 * 	&lt;/ul&gt;
 *
 *	&lt;br&gt;&lt;br&gt;
 *  &lt;ul&gt;
 *		&lt;li&gt;&lt;b&gt;Module &lt;/b&gt; = &lt;a href = &quot;https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md&quot;&gt;Computational Core Module&lt;/a&gt;&lt;/li&gt;
 *		&lt;li&gt;&lt;b&gt;Library&lt;/b&gt; = &lt;a href = &quot;https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md&quot;&gt;Function Analysis Library&lt;/a&gt;&lt;/li&gt;
 *		&lt;li&gt;&lt;b&gt;Project&lt;/b&gt; = &lt;a href = &quot;https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md&quot;&gt;Special Function Implementation Analysis&lt;/a&gt;&lt;/li&gt;
 *		&lt;li&gt;&lt;b&gt;Package&lt;/b&gt; = &lt;a href = &quot;https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/bessel/README.md&quot;&gt;Ordered Bessel Function Variant Estimators&lt;/a&gt;&lt;/li&gt;
 *  &lt;/ul&gt;
 *
 * @author Lakshmi Krishnamurthy
 */

public abstract class SecondWatsonIntegralEstimator extends
	org.drip.specialfunction.definition.BesselSecondKindEstimator
{
<span class="nc" id="L119">	private int _quadratureCount = -1;</span>

	/**
	 * Construct the Bessel Second Kind Estimator from the Watson Integer Integral Form
	 * 
	 * @param quadratureCount Count of the Integrand Quadrature
	 * 
	 * @return Bessel Second Kind Estimator from the Watson Integer Integral Form
	 */

	public static final SecondWatsonIntegralEstimator IntegerForm (
		final int quadratureCount)
	{
		try
		{
<span class="nc" id="L134">			return new SecondWatsonIntegralEstimator (quadratureCount)</span>
<span class="nc" id="L135">			{</span>
				@Override public double bigY (
					final double alpha,
					final double z)
					throws java.lang.Exception
				{
<span class="nc bnc" id="L141" title="All 2 branches missed.">					if (!org.drip.numerical.common.NumberUtil.IsInteger (alpha) ||</span>
<span class="nc bnc" id="L142" title="All 2 branches missed.">						!org.drip.numerical.common.NumberUtil.IsValid (z))</span>
					{
<span class="nc" id="L144">						throw new java.lang.Exception</span>
							(&quot;SecondWatsonIntegralEstimator::IntegerForm::evaluate =&gt; Invalid Inputs &quot; + alpha);
					}

<span class="nc" id="L148">					return (org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (</span>
						0.,
						java.lang.Math.PI,
						quadratureCount
<span class="nc" id="L152">					).integrate (</span>
						new org.drip.function.definition.R1ToR1 (null)
<span class="nc" id="L154">						{</span>
							@Override public double evaluate (
								final double theta)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L159" title="All 2 branches missed.">								if (java.lang.Double.isInfinite (theta))</span>
								{
<span class="nc" id="L161">									return 0.;</span>
								}

<span class="nc" id="L164">								return java.lang.Math.sin (z * java.lang.Math.sin (theta) - alpha * theta);</span>
							}
						}
					) / java.lang.Math.PI) -
<span class="nc" id="L168">					org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (</span>
						0.,
						quadratureCount
<span class="nc" id="L171">					).integrate (</span>
						new org.drip.function.definition.R1ToR1 (null)
<span class="nc" id="L173">						{</span>
							@Override public double evaluate (
								final double t)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L178" title="All 2 branches missed.">								if (java.lang.Double.isInfinite (t))</span>
								{
<span class="nc" id="L180">									return 0.;</span>
								}

<span class="nc" id="L183">								double ePowerAlphaT = java.lang.Math.exp (alpha * t);</span>

<span class="nc bnc" id="L185" title="All 2 branches missed.">								double expPrefix = 0 == (alpha % 2) ? ePowerAlphaT + 1. / ePowerAlphaT :</span>
									ePowerAlphaT - 1. / ePowerAlphaT;

<span class="nc" id="L188">								return expPrefix * java.lang.Math.exp (-z * java.lang.Math.sinh (t));</span>
							}
						}
					) / java.lang.Math.PI;
				}
			};
		}
<span class="nc" id="L195">		catch (java.lang.Exception e)</span>
		{
<span class="nc" id="L197">			e.printStackTrace();</span>
		}

<span class="nc" id="L200">		return null;</span>
	}

	protected SecondWatsonIntegralEstimator (
		final int quadratureCount)
		throws java.lang.Exception
<span class="nc" id="L206">	{</span>
<span class="nc bnc" id="L207" title="All 2 branches missed.">		if (0 &gt;= (_quadratureCount = quadratureCount))</span>
		{
<span class="nc" id="L209">			throw new java.lang.Exception (&quot;SecondWatsonIntegralEstimator Constructor =&gt; Invalid Inputs&quot;);</span>
		}
<span class="nc" id="L211">	}</span>

	/**
	 * Retrieve the Quadrature Count
	 * 
	 * @return The Quadrature Count
	 */

	public int quadratureCount()
	{
<span class="nc" id="L221">		return _quadratureCount;</span>
	}
}
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