LogFactorialEstimateNemesCorrection.java
package org.drip.sample.stirling;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.common.NumberUtil;
import org.drip.numerical.estimation.R1Estimate;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.loggamma.StirlingSeriesEstimator;
/*
* -*- 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>LogFactorialEstimateNemesCorrection</i> illustrates the Nemes Correction applied to the Stirling's
* Approximation of the Log Factorial Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function <i>Computers and
* Mathematics with Applications</i> <b>61 (11)</b> 3364-3369
* </li>
* <li>
* National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical
* Functions https://dlmf.nist.gov/5.11
* </li>
* <li>
* Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n!
* https://arxiv.org/abs/1003.2907 <b>arXiv</b>
* </li>
* <li>
* Toth V. T. (2016): Programmable Calculators – The Gamma Function
* http://www.rskey.org/CMS/index.php/the-library/11
* </li>
* <li>
* Wikipedia (2019): Stirling's Approximation
* https://en.wikipedia.org/wiki/Stirling%27s_approximation
* </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/feed/README.md">Function</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/stirling/README.md">Stirling Approximation Based Gamma Estimates</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class LogFactorialEstimateNemesCorrection
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int factorialCount = 12;
StirlingSeriesEstimator logFactorial = new StirlingSeriesEstimator (null);
System.out.println ("\t|--------------------------------------------------||");
System.out.println ("\t| STIRLING LOG FACTORIAL NEMES CORRECTION ||");
System.out.println ("\t|--------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Factorial Index ||");
System.out.println ("\t| - Stirling's Estimate ||");
System.out.println ("\t| - Nemes' Correction ||");
System.out.println ("\t| - Corrected Stirling's Estimate ||");
System.out.println ("\t| - Log Factorial Value ||");
System.out.println ("\t|--------------------------------------------------||");
for (int factorialIndex = 1; factorialIndex <= factorialCount; ++factorialIndex)
{
R1Estimate numericalApproximation = logFactorial.nemesCorrectionEstimate
(factorialIndex);
double zeroOrder = numericalApproximation.baseline();
double totalCorrection = numericalApproximation.seriesCumulative();
System.out.println (
"\t| " + FormatUtil.FormatDouble (factorialIndex, 2, 0, 1.) + " => " +
FormatUtil.FormatDouble (zeroOrder, 2, 4, 1.) + " | " +
FormatUtil.FormatDouble (totalCorrection, 2, 4, 1.) + " | " +
FormatUtil.FormatDouble (zeroOrder + totalCorrection, 2, 4, 1.) + " | " +
FormatUtil.FormatDouble (Math.log (NumberUtil.Factorial (factorialIndex)), 2, 4, 1.) + " ||"
);
}
System.out.println ("\t|--------------------------------------------------||");
System.out.println();
System.out.println ("\t|------------------------------------------------------------||");
System.out.println ("\t| STIRLING FACTORIAL NEMES CORRECTION ||");
System.out.println ("\t|------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Factorial Index ||");
System.out.println ("\t| - Nemes' First Order Correction ||");
System.out.println ("\t| - Nemes' Third Order Correction ||");
System.out.println ("\t| - Nemes' Fifth Order Correction ||");
System.out.println ("\t| - Nemes' Seventh Order Correction ||");
System.out.println ("\t|------------------------------------------------------------||");
for (int factorialIndex = 1; factorialIndex <= factorialCount; ++factorialIndex)
{
R1Estimate numericalApproximation = logFactorial.nemesCorrectionEstimate
(factorialIndex);
double firstOrderCorrection = numericalApproximation.orderSeries (1);
double thirdOrderCorrection = numericalApproximation.orderSeries (3);
double fifthOrderCorrection = numericalApproximation.orderSeries (5);
double seventhOrderCorrection = numericalApproximation.orderSeries (7);
double totalCorrection = firstOrderCorrection + thirdOrderCorrection + fifthOrderCorrection +
seventhOrderCorrection;
System.out.println (
"\t|" + FormatUtil.FormatDouble (factorialIndex, 2, 0, 1.) + " => " +
FormatUtil.FormatDouble (firstOrderCorrection, 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (thirdOrderCorrection, 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (fifthOrderCorrection, 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (seventhOrderCorrection, 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (totalCorrection, 1, 5, 1.) + " ||"
);
}
System.out.println ("\t|------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}