ERFCInverseFactorialExpansion.java

package org.drip.sample.erfx;

import java.util.Map;

import org.drip.function.e2erf.BuiltInEntry;
import org.drip.function.e2erfc.ErrorFunctionComplement;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

/*
 * -*- 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>ERFCInverseFactorialExpansion</i> illustrates the Error Function Complement Estimation based on the
 * Inverse Factorial Expansion Error Function Complement Series. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
 *              on Mathematics</b>
 *      </li>
 *      <li>
 *          Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
 *              Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
 *      </li>
 *      <li>
 *          Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
 *              Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
 *              22-32
 *      </li>
 *      <li>
 *          Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
 *              Linear and Non-linear Heat Transfer and Diffusion
 *              https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
 *      </li>
 *      <li>
 *          Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_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/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/erfx/README.md">E<sup>2</sup> erfc and erfi Estimation</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ERFCInverseFactorialExpansion
{

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

        Map<Double, BuiltInEntry> builtInTable = BuiltInEntry.Table();

        int termCount = 70;

        ErrorFunctionComplement erfInverseFactorial = ErrorFunctionComplement.InverseFactorialExpansion
            (termCount);

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

        System.out.println ("\t|      Inverse Factorial Expansion erfc Estimate      ||");

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

        System.out.println ("\t|        L -> R:                                      ||");

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

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

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

        System.out.println ("\t|                - Inverse Factorial Estimate Error   ||");

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

        for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
        {
            double x = builtInTableEntry.getKey();

            double erfcTable = builtInTableEntry.getValue().erfc();

            double erfcEstimate = erfInverseFactorial.evaluate (x);

            System.out.println (
                "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
                FormatUtil.FormatDouble (erfcTable, 1, 9, 1.) + " | " +
                FormatUtil.FormatDouble (erfcEstimate, 1, 9, 1.) + " | " +
                FormatUtil.FormatDouble (Math.abs (erfcEstimate - erfcTable), 1, 9, 1.) + " ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}