BernsteinBinetBoundProperty.java
package org.drip.sample.digamma;
import org.drip.function.definition.R1PropertyVerification;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.property.DigammaInequalityLemma;
/*
* -*- 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>BernsteinBinetBoundProperty</i> demonstrates the Estimation of the Bernstein-Binet Bounds of the
* Digamma Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
* Mathematics</b>
* </li>
* <li>
* Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
* Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
* </li>
* <li>
* Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
* Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
* </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): Digamma Function https://en.wikipedia.org/wiki/Digamma_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/digamma/README.md">Estimates of the Digamma Function</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class BernsteinBinetBoundProperty
{
private static final void Verifier (
final double z)
throws Exception
{
R1PropertyVerification leftVerification = DigammaInequalityLemma.BernsteinBinetLeftBound().verify (z);
R1PropertyVerification rightVerification = DigammaInequalityLemma.BernsteinBinetRightBound().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() + " ||"
);
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] zArray =
{
0.25,
0.50,
0.75,
1.00,
1.25,
1.50,
2.00,
2.50,
3.00,
3.50,
4.00,
4.50,
5.00,
5.50,
6.00,
6.50,
7.00,
7.50,
8.00,
8.50,
9.00,
9.50,
};
System.out.println ("\t|----------------------------------------------------------------------||");
System.out.println ("\t| DIGAMMA FUNCTION BERNSTEIN-BINET BOUND PROPERTY ||");
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|----------------------------------------------------------------------||");
for (double z : zArray)
{
Verifier (z);
}
System.out.println ("\t|----------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}