jacoco/org.drip.specialfunction.bessel/ModifiedSecondIntegralEstimator.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;ModifiedSecondIntegralEstimator&lt;/i&gt; implements the Integral Estimator for the Modified 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 ModifiedSecondIntegralEstimator extends
	org.drip.specialfunction.definition.ModifiedBesselSecondKindEstimator
{
<span class="nc" id="L119">	private int _quadratureCount = -1;</span>

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

	public static final ModifiedSecondIntegralEstimator Standard (
		final int quadratureCount)
	{
		try
		{
<span class="nc" id="L134">			return new ModifiedSecondIntegralEstimator (quadratureCount)</span>
<span class="nc" id="L135">			{</span>
				@Override public double bigK (
					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.IsValid (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;ModifiedSecondIntegralEstimator::Standard::evaluate =&gt; Invalid Inputs&quot;);
					}

<span class="nc" id="L148">					return</span>
<span class="nc" id="L149">					org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (</span>
						0.,
						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 t)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L159" title="All 2 branches missed.">								return java.lang.Double.isInfinite (t) ? 0. :</span>
<span class="nc" id="L160">									java.lang.Math.exp (-z * java.lang.Math.cosh (t)) *</span>
<span class="nc" id="L161">										java.lang.Math.cosh (alpha * t);</span>
							}
						}
					);
				}
			};
		}
<span class="nc" id="L168">		catch (java.lang.Exception e)</span>
		{
<span class="nc" id="L170">			e.printStackTrace();</span>
		}

<span class="nc" id="L173">		return null;</span>
	}

	/**
	 * Construct the Modified Bessel Second Kind Zero Order Estimator from the Integral Form
	 * 
	 * @param quadratureCount Count of the Integrand Quadrature
	 * 
	 * @return Modified Bessel Second Kind Zero Order Estimator from the Integral Form
	 */

	public static final ModifiedSecondIntegralEstimator ZeroOrder (
		final int quadratureCount)
	{
		try
		{
<span class="nc" id="L189">			return new ModifiedSecondIntegralEstimator (quadratureCount)</span>
<span class="nc" id="L190">			{</span>
				@Override public double bigK (
					final double alpha,
					final double z)
					throws java.lang.Exception
				{
<span class="nc bnc" id="L196" title="All 2 branches missed.">					if (0. != alpha ||</span>
<span class="nc bnc" id="L197" title="All 2 branches missed.">						!org.drip.numerical.common.NumberUtil.IsValid (z))</span>
					{
<span class="nc" id="L199">						throw new java.lang.Exception</span>
							(&quot;ModifiedSecondIntegralEstimator::ZeroOrder::evaluate =&gt; Invalid Inputs&quot;);
					}

<span class="nc" id="L203">					return 0.5 * org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussHermite (</span>
						quadratureCount
<span class="nc" id="L205">					).integrate (</span>
						new org.drip.function.definition.R1ToR1 (null)
<span class="nc" id="L207">						{</span>
							@Override public double evaluate (
								final double t)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L212" title="All 2 branches missed.">								return java.lang.Double.isInfinite (t) ? 0. :</span>
<span class="nc" id="L213">									java.lang.Math.cos (z * t) / java.lang.Math.sqrt (t * t + 1.);</span>
							}
						}
					);
				}
			};
		}
<span class="nc" id="L220">		catch (java.lang.Exception e)</span>
		{
<span class="nc" id="L222">			e.printStackTrace();</span>
		}

<span class="nc" id="L225">		return null;</span>
	}

	/**
	 * Construct the Modified Bessel Second Kind Estimator for the 1. / 3. Order from the Integral Form
	 * 
	 * @param quadratureCount Count of the Integrand Quadrature
	 * 
	 * @return Modified Bessel Second Kind Estimator for the 1. / 3. Order from the Integral Form
	 */

	public static final ModifiedSecondIntegralEstimator OneThirdOrder (
		final int quadratureCount)
	{
		try
		{
<span class="nc" id="L241">			return new ModifiedSecondIntegralEstimator (quadratureCount)</span>
<span class="nc" id="L242">			{</span>
				@Override public double bigK (
					final double alpha,
					final double z)
					throws java.lang.Exception
				{
<span class="nc bnc" id="L248" title="All 2 branches missed.">					if (1. / 3. != 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>
							(&quot;ModifiedSecondIntegralEstimator::OneThirdOrder::evaluate =&gt; Invalid Inputs&quot;);
					}

<span class="nc" id="L255">					return java.lang.Math.sqrt (3.) *</span>
<span class="nc" id="L256">					org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (</span>
						0.,
						quadratureCount
<span class="nc" id="L259">					).integrate (</span>
						new org.drip.function.definition.R1ToR1 (null)
<span class="nc" id="L261">						{</span>
							@Override public double evaluate (
								final double x)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L266" title="All 2 branches missed.">								if (java.lang.Double.isInfinite (x))</span>
								{
<span class="nc" id="L268">									return 0.;</span>
								}

<span class="nc" id="L271">								double xSquaredOver3 = x * x / 3.;</span>

<span class="nc" id="L273">								return java.lang.Math.exp (</span>
<span class="nc" id="L274">									-z * (1. + 4. * xSquaredOver3) * java.lang.Math.sqrt (1. + xSquaredOver3)</span>
								);
							}
						}
					);
				}
			};
		}
<span class="nc" id="L282">		catch (java.lang.Exception e)</span>
		{
<span class="nc" id="L284">			e.printStackTrace();</span>
		}

<span class="nc" id="L287">		return null;</span>
	}

	/**
	 * Construct the Modified Bessel Second Kind Estimator for the 2. / 3. Order from the Integral Form
	 * 
	 * @param quadratureCount Count of the Integrand Quadrature
	 * 
	 * @return Modified Bessel Second Kind Estimator for the 2. / 3. Order from the Integral Form
	 */

	public static final ModifiedSecondIntegralEstimator TwoThirdOrder (
		final int quadratureCount)
	{
		try
		{
<span class="nc" id="L303">			return new ModifiedSecondIntegralEstimator (quadratureCount)</span>
<span class="nc" id="L304">			{</span>
				@Override public double bigK (
					final double alpha,
					final double z)
					throws java.lang.Exception
				{
<span class="nc bnc" id="L310" title="All 2 branches missed.">					if (2. / 3. != alpha ||</span>
<span class="nc bnc" id="L311" title="All 2 branches missed.">						!org.drip.numerical.common.NumberUtil.IsValid (z))</span>
					{
<span class="nc" id="L313">						throw new java.lang.Exception</span>
							(&quot;ModifiedSecondIntegralEstimator::TwoThirdOrder::evaluate =&gt; Invalid Inputs&quot;);
					}

<span class="nc" id="L317">					return 1. / java.lang.Math.sqrt (3.) *</span>
<span class="nc" id="L318">					org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (</span>
						0.,
						quadratureCount
<span class="nc" id="L321">					).integrate (</span>
						new org.drip.function.definition.R1ToR1 (null)
<span class="nc" id="L323">						{</span>
							@Override public double evaluate (
								final double x)
								throws java.lang.Exception
							{
<span class="nc bnc" id="L328" title="All 2 branches missed.">								if (java.lang.Double.isInfinite (x))</span>
								{
<span class="nc" id="L330">									return 0.;</span>
								}

<span class="nc" id="L333">								double xSquared = x * x;</span>
<span class="nc" id="L334">								double xSquaredOver3 = xSquared / 3.;</span>

<span class="nc" id="L336">								double sqrt_OnePlusXSquaredOver3_ = java.lang.Math.sqrt (1. + xSquaredOver3);</span>

<span class="nc" id="L338">								return (3. + 2. * xSquared) / sqrt_OnePlusXSquaredOver3_ *</span>
<span class="nc" id="L339">									java.lang.Math.exp (</span>
										-z * (1. + 4. * xSquaredOver3) * sqrt_OnePlusXSquaredOver3_
									);
							}
						}
					);
				}
			};
		}
<span class="nc" id="L348">		catch (java.lang.Exception e)</span>
		{
<span class="nc" id="L350">			e.printStackTrace();</span>
		}

<span class="nc" id="L353">		return null;</span>
	}

	protected ModifiedSecondIntegralEstimator (
		final int quadratureCount)
		throws java.lang.Exception
<span class="nc" id="L359">	{</span>
<span class="nc bnc" id="L360" title="All 2 branches missed.">		if (0 &gt;= (_quadratureCount = quadratureCount))</span>
		{
<span class="nc" id="L362">			throw new java.lang.Exception (&quot;ModifiedSecondIntegralEstimator Constructor =&gt; Invalid Inputs&quot;);</span>
		}
<span class="nc" id="L364">	}</span>

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

	public int quadratureCount()
	{
<span class="nc" id="L374">		return _quadratureCount;</span>
	}
}
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