EnERFMacLaurin.java
package org.drip.sample.erf;
import org.drip.function.enerf.GeneralizedErrorFunction;
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>EnERFMacLaurin</i> illustrates the MacLaurin Series Based Estimates for E<sub>n</sub> erf. 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 EnERFMacLaurin
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] xArray =
{
-3.25,
-3.00,
-2.75,
-2.50,
-2.25,
-2.00,
-1.75,
-1.50,
-1.25,
-1.00,
-0.75,
-0.50,
-0.25,
0.00,
0.25,
0.50,
0.75,
1.00,
1.25,
1.50,
1.75,
2.00,
2.25,
2.50,
2.75,
3.00,
3.25
};
int[] degreeArray =
{
0,
1,
2,
3,
4,
5
};
int termCount = 50;
GeneralizedErrorFunction[] erfnArray = new GeneralizedErrorFunction[degreeArray.length];
for (int degree : degreeArray)
{
erfnArray[degree] = GeneralizedErrorFunction.MacLaurin (
degree,
termCount
);
}
System.out.println ("\t|-----------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| E_n MacLaurin erf Estimate ||");
System.out.println ("\t|-----------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - x ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 0) ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 1) ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 2) ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 3) ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 4) ||");
System.out.println ("\t| - MacLaurin Estimate (Degree = 5) ||");
System.out.println ("\t|-----------------------------------------------------------------------------------------------------------------------------------------------------------------||");
for (double x : xArray)
{
System.out.println (
"\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (erfnArray[0].evaluate (x), 1, 2, 1.) + " | " +
FormatUtil.FormatDouble (erfnArray[1].evaluate (x), 2, 2, 1.) + " | " +
FormatUtil.FormatDouble (erfnArray[2].evaluate (x), 1, 2, 1.) + " | " +
FormatUtil.FormatDouble (erfnArray[3].evaluate (x), 14, 0, 1.) + " | " +
FormatUtil.FormatDouble (erfnArray[4].evaluate (x), 38, 0, 1.) + " | " +
FormatUtil.FormatDouble (erfnArray[5].evaluate (x), 64, 0, 1.) + " ||"
);
}
System.out.println ("\t|-----------------------------------------------------------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}