FourierBlagouchineSeriesEstimate.java
package org.drip.sample.gamma;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.loggamma.InfiniteSumEstimator;
/*
* -*- 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>FourierBlagouchineSeriesEstimate</i> demonstrates the Estimate of the Log Gamma Function using the
* Malmsten-Blagouchine as well as the Blagouchine (2015) Variants of the Fourier Series Expansion. 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 FourierBlagouchineSeriesEstimate
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int fourierTermCount = 1000000;
int blagouchineTermCount = 10000;
double[] sArray =
{
0.05,
0.10,
0.15,
0.20,
0.25,
0.30,
0.35,
0.40,
0.45,
// 0.50,
0.55,
0.60,
0.65,
0.70,
0.75,
0.80,
0.85,
0.90,
0.95,
};
InfiniteSumEstimator fourier = InfiniteSumEstimator.Fourier (fourierTermCount);
InfiniteSumEstimator blagouchine = InfiniteSumEstimator.Blagouchine2015 (blagouchineTermCount);
System.out.println ("\t|---------------------------------------------------------------------------||");
System.out.println ("\t| MALMSTEN-BLAGOUCHINE FOURIER SERIES GAMMA ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - s ||");
System.out.println ("\t| - Malmsten-Blagouchine Fourier Series Log Gamma ||");
System.out.println ("\t| - Blagouchine (2015) Fourier Series Log Gamma ||");
System.out.println ("\t| - Malmsten-Blagouchine Fourier Series Gamma ||");
System.out.println ("\t| - Blagouchine (2015) Fourier Series Gamma ||");
System.out.println ("\t|---------------------------------------------------------------------------||");
for (double s : sArray)
{
double fourierLogGamma = fourier.evaluate (s);
double blagouchineLogGamma = blagouchine.evaluate (s);
System.out.println (
"\t|" + FormatUtil.FormatDouble (s, 1, 2, 1.) + " => {" +
FormatUtil.FormatDouble (fourierLogGamma, 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (blagouchineLogGamma, 1, 10, 1.) + "} {" +
FormatUtil.FormatDouble (Math.exp (fourierLogGamma), 2, 10, 1.) + " | " +
FormatUtil.FormatDouble (Math.exp (blagouchineLogGamma), 2, 10, 1.) + "} ||"
);
}
System.out.println ("\t|---------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}