ModifiedFirstHankelAsymptote.java
package org.drip.sample.bessel;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator;
import org.drip.specialfunction.bessel.ModifiedFirstHankelAsymptoteEstimator;
import org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator;
import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
/*
* -*- 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>ModifiedFirstHankelAsymptote</i> illustrates the Large z Hankel Asymptote Series Based Estimation for
* the Modified 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/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/bessel/README.md">Estimates of the Bessel Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ModifiedFirstHankelAsymptote
{
private static final void BesselI (
final ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator,
final double[] zArray,
final double[] alphaArray)
throws Exception
{
System.out.println ("\t|---------------------------------------------------------------------------||");
System.out.println ("\t| MODIFIED BESSEL FIRST KIND ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - z ||");
System.out.println ("\t| - Alpha Bessel Estimate Row ||");
System.out.println ("\t|---------------------------------------------------------------------------||");
for (double z : zArray)
{
String display = "\t| [" + FormatUtil.FormatDouble (z, 2, 1, 1., false) + "] => ";
for (double alpha : alphaArray)
{
display = display + " " + FormatUtil.FormatDouble (
modifiedBesselFirstKindEstimator.bigI (
alpha,
z
), 2, 6, 1.
) + " |";
}
System.out.println (display + "|");
}
System.out.println ("\t|---------------------------------------------------------------------------||");
System.out.println();
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int frobeniusTermCount = 40;
int hankelAsymptoteTermCount = 4;
double[] zArray =
{
2.,
4.,
6.,
8.,
10.,
12.,
14.,
};
double[] alphaArray =
{
0.0,
1.0,
2.0,
3.0,
4.0,
};
BesselI (
ModifiedFirstFrobeniusSeriesEstimator.Standard (
new EulerIntegralSecondKind (null),
frobeniusTermCount
),
zArray,
alphaArray
);
BesselI (
ModifiedFirstHankelAsymptoteEstimator.Standard (hankelAsymptoteTermCount),
zArray,
alphaArray
);
EnvManager.TerminateEnv();
}
}