LowerSHalfEstimate.java
package org.drip.sample.gammaincomplete;
import org.drip.function.e2erf.AbramowitzStegun;
import org.drip.function.e2erf.ErrorFunctionAnalytical;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
* calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
* FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three main modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* 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
* - 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>LowerSHalfEstimate</i> illustrates the Estimation of the Lower Incomplete Gamma Function using the NIST
* (2019) Series for s = 0.5. The References are:
*
* <br><br>
* <ul>
* <li>
* Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
* Definite Integrals involving Elementary Functions via Differentiation of Special Functions
* <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
* </li>
* <li>
* Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
* <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
* </li>
* <li>
* Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
* e<sup>iπx</sup> x<sup>(1/x)</sup> between 1 and ∞
* https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
* </li>
* <li>
* National Institute of Standards and Technology (2019a): Incomplete Gamma and Related Functions
* https://dlmf.nist.gov/8
* </li>
* <li>
* Wikipedia (2019): Incomplete Gamma Function
* https://en.wikipedia.org/wiki/Incomplete_gamma_function
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gammaincomplete/README.md">Estimates of Incomplete Gamma Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class LowerSHalfEstimate
{
private static final void EulerIntegralComparison (
final int termCount,
final double[] zArray)
throws Exception
{
System.out.println ("\t|----------------------------------------||");
System.out.println ("\t| TERM COUNT => " + FormatUtil.FormatDouble (termCount, 2, 0, 1.));
System.out.println ("\t|----------------------------------------||");
System.out.println ("\t| L - R: ||");
System.out.println ("\t| - Integral Estimate ||");
System.out.println ("\t| - erf Estimate ||");
System.out.println ("\t|----------------------------------------||");
AbramowitzStegun erfWinitzki = ErrorFunctionAnalytical.Winitzki2008b();
for (double z : zArray)
{
LowerEulerIntegral lowerEulerIntegral = new LowerEulerIntegral (
null,
z
);
System.out.println (
"\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
FormatUtil.FormatDouble (lowerEulerIntegral.evaluate (0.5), 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (Math.sqrt (Math.PI) * erfWinitzki.evaluate (Math.sqrt (z)), 1, 10, 1.) + " ||"
);
}
System.out.println ("\t|----------------------------------------||");
System.out.println();
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int termCount = 50;
double[] zArray =
{
40.00,
35.00,
30.00,
25.00,
20.00,
15.00,
10.00,
5.00,
4.00,
3.00,
2.00,
1.00,
0.01,
};
EulerIntegralComparison (
termCount,
zArray
);
EnvManager.TerminateEnv();
}
}