GautschiConvexProperty.java
package org.drip.sample.gamma;
import org.drip.function.definition.R1ToR1Property;
import org.drip.function.definition.R1PropertyVerification;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.property.GammaInequalityLemma;
/*
* -*- 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>GautschiConvexProperty</i> demonstrates the Verification of the Gautschi Double-Bound Convex Property
* of the Gamma Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour
* Integration Methods, and some Related Results <i>Ramanujan Journal</i> <b>35 (1)</b> 21-110
* </li>
* <li>
* Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly
* https://arxiv.org/abs/1703.05349 <b>arXiv</b>
* </li>
* <li>
* Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
* <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
* </li>
* <li>
* Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
* University Press</b> New York
* </li>
* <li>
* Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/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/gamma/README.md">Integrand Estimates of Gamma Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class GautschiConvexProperty
{
private static final void Verifier (
final double s,
final double[] zArray)
throws Exception
{
System.out.println ("\t|----------------------------------------------------------------------||");
System.out.println ("\t| GAMMA FUNCTION GAUTSCHI CONVEX PROPERTY ||");
System.out.println ("\t| s = " + FormatUtil.FormatDouble (s, 1, 1, 1.));
System.out.println ("\t|----------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - z ||");
System.out.println ("\t| - LHS Value ||");
System.out.println ("\t| - Middle Value ||");
System.out.println ("\t| - RHS Value ||");
System.out.println ("\t| - Left Verification Success? ||");
System.out.println ("\t| - Right Verification Success? ||");
System.out.println ("\t|----------------------------------------------------------------------||");
R1ToR1Property gautschiLeftProperty = GammaInequalityLemma.GautschiLeft (s);
R1ToR1Property gautschiRightProperty = GammaInequalityLemma.GautschiRight (s);
for (double z : zArray)
{
R1PropertyVerification leftVerification = gautschiLeftProperty.verify (z);
R1PropertyVerification rightVerification = gautschiRightProperty.verify (z);
System.out.println (
"\t|" + FormatUtil.FormatDouble (z, 2, 2, 1.) + " => " +
FormatUtil.FormatDouble (leftVerification.lValue(), 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (leftVerification.rValue(), 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (rightVerification.rValue(), 1, 10, 1.) + " | " +
leftVerification.verified() + " | " +
rightVerification.verified() + " ||"
);
}
System.out.println ("\t|----------------------------------------------------------------------||");
System.out.println();
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] sArray =
{
0.1,
0.2,
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
};
double[] zArray =
{
1.5,
2.0,
2.5,
3.0,
3.5,
4.0,
4.5,
5.0,
5.5,
6.0,
6.5,
7.0,
7.5,
8.0,
8.5,
9.0,
9.5,
};
for (double s : sArray)
{
Verifier (
s,
zArray
);
}
EnvManager.TerminateEnv();
}
}