FactorialEstimateLaplaceCorrection.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.gamma.StirlingSeries;

/*
 * -*- 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>FactorialEstimateLaplaceCorrection</i> illustrates the Laplace Correction applied to the Stirling's
 * Approximation of the 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 FactorialEstimateLaplaceCorrection
{

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int factorialCount = 12;

        StirlingSeries stirlingFactorial = new StirlingSeries (null);

        System.out.println ("\t|------------------------------------------------------------||");

        System.out.println ("\t|              STIRLING FACTORIAL APPROXIMATION              ||");

        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|              - Laplace's Correction                        ||");

        System.out.println ("\t|              - Corrected Stirling's Estimate               ||");

        System.out.println ("\t|              - Factorial Value                             ||");

        System.out.println ("\t|------------------------------------------------------------||");

        for (int factorialIndex = 1; factorialIndex <= factorialCount; ++factorialIndex)
        {
            R1Estimate numericalApproximation = stirlingFactorial.laplaceCorrectionEstimate
                (factorialIndex);

            double zeroOrder = numericalApproximation.baseline();

            double firstOrderCorrection = numericalApproximation.orderSeries (1);

            System.out.println (
                "\t| " + factorialIndex + " => " +
                FormatUtil.FormatDouble (zeroOrder + 0.5, 1, 0, 1.) + " | " +
                FormatUtil.FormatDouble (firstOrderCorrection + 0.5, 1, 0, 1.) + " | " +
                FormatUtil.FormatDouble (zeroOrder + firstOrderCorrection + 0.5, 1, 0, 1.) + " | " +
                NumberUtil.Factorial (factorialIndex) + " ||"
            );
        }

        System.out.println ("\t|------------------------------------------------------------||");

        EnvManager.TerminateEnv();
    }
}