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();
- }
- }