ERFHansHeinrichBurmannConvergent.java
package org.drip.sample.erf;
import java.util.Map;
import org.drip.function.e2erf.BuiltInEntry;
import org.drip.function.e2erf.ErrorFunction;
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>ERFHansHeinrichBurmannConvergent</i> illustrates the Error Function Estimation based on the Convergent
* Hans-Heinrich-Burmann 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/erf/README.md">E<sup>2</sup> and E<sup>n</sup> erf Estimation</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ERFHansHeinrichBurmannConvergent
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
Map<Double, BuiltInEntry> builtInTable = BuiltInEntry.Table();
ErrorFunction erfHansHeinrichBurmannConvergent = ErrorFunction.HansHeinrichBurmannConvergent();
System.out.println ("\t|-----------------------------------------------------||");
System.out.println ("\t| Hans Heinrich Burmann erf 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| - Hans Heinrich Burmann Estimate ||");
System.out.println ("\t| - Hans Heinrich Burmann Error ||");
System.out.println ("\t|-----------------------------------------------------||");
for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
{
double x = builtInTableEntry.getKey();
double erfTable = builtInTableEntry.getValue().erf();
double erfEstimate = erfHansHeinrichBurmannConvergent.evaluate (x);
System.out.println (
"\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (erfTable, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfEstimate, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (Math.abs (erfEstimate - erfTable), 1, 9, 1.) + " ||"
);
}
System.out.println ("\t|-----------------------------------------------------||");
EnvManager.TerminateEnv();
}
}