ErrorFunctionAnalytical.java

package org.drip.function.e2erf;

/*
 * -*- 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>ErrorFunctionAnalytical</i> implements Analytical Versions of the E<sub>2</sub> Error Function (erf)
 * Estimate. 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/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/e2erf/README.md">E<sub>2</sub> erf and erf<sup>-1</sup> Implementations</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ErrorFunctionAnalytical
{

    /**
     * Construct Winitzki (2008) Version of the E<sub>2</sub> erf Analytical
     * 
     * @param a a
     * @param maximumError Maximum Absolute Error
     * 
     * @return Winitzki (2008) Version of the E<sub>2</sub> erf Analytical
     */

    public static final org.drip.function.e2erf.AbramowitzStegun Winitzki2008 (
        final double a,
        final double maximumError)
    {
        try
        {
            return !org.drip.numerical.common.NumberUtil.IsValid (a) ? null :
                new org.drip.function.e2erf.AbramowitzStegun (
                    null,
                    null,
                    maximumError
                )
            {
                @Override public double evaluate (
                    final double z)
                    throws java.lang.Exception
                {
                    if (!org.drip.numerical.common.NumberUtil.IsValid (z))
                    {
                        throw new java.lang.Exception
                            ("ErrorFunctionAnalytical::Winitzki2008::evaluate => Invalid Inputs");
                    }

                    if (0. == z)
                    {
                        return 0.;
                    }

                    if (z < 0)
                    {
                        return -1. * evaluate (-1. * z);
                    }

                    double z2 = z * z;
                    double az2 = a * z * z;

                    return java.lang.Math.sqrt (1. - java.lang.Math.exp (
                        -1. * z2 * (az2 + (4. / java.lang.Math.PI)) / (az2 + 1.))
                    );
                }
            };
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct Winitzki (2008a) Version of E<sub>2</sub> erf Analytical
     * 
     * @return Winitzki (2008a) Version of E<sub>2</sub> erf Analytical
     */

    public static final org.drip.function.e2erf.AbramowitzStegun Winitzki2008a()
    {
        return Winitzki2008 (
            8. * (java.lang.Math.PI - 3.) / (3. * java.lang.Math.PI * (4. - java.lang.Math.PI)),
            0.00035
        );
    }

    /**
     * Construct Winitzki (2008b) Version of E<sub>2</sub> erf Analytical
     * 
     * @return Winitzki (2008b) Version of E<sub>2</sub> erf Analytical
     */

    public static final org.drip.function.e2erf.AbramowitzStegun Winitzki2008b()
    {
        return Winitzki2008 (
            0.147,
            0.00012
        );
    }
}