ERFCCraig1991G7K15.java
package org.drip.sample.gausskronrod;
import java.util.Map;
import org.drip.function.definition.R1ToR1;
import org.drip.function.e2erf.BuiltInEntry;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.integration.GaussKronrodQuadratureGenerator;
import org.drip.numerical.integration.QuadratureEstimate;
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>ERFCCraig1991G7K15</i> computes the R<sup>1</sup> Nested Numerical Estimate and Error of the erfc
* Integrand using the G7-K15 Gaussian Integration Quadrature Scheme. The References are:
*
* <br><br>
* <ul>
* <li>
* Holoborodko, P. (2011): Gauss-Kronrod Quadrature Nodes and Weights
* https://www.advanpix.com/2011/11/07/gauss-kronrod-quadrature-nodes-weights/
* </li>
* <li>
* Kahaner, D., C. Moler, and S. Nash (1989): <i>Numerical Methods and Software</i> <b>Prentice
* Hall</b>
* </li>
* <li>
* Laurie, D. (1997): Calculation of Gauss-Kronrod Quadrature Rules <i>Mathematics of
* Computation</i> <b>66 (219)</b> 1133-1145
* </li>
* <li>
* Piessens, R., E. de Doncker-Kapenga, C. W. Uberhuber, and D. K. Kahaner (1983): <i>QUADPACK – A
* Subroutine Package for Automatic Integration</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Wikipedia (2019): Gauss-Kronrod Quadrature Formula
* https://en.wikipedia.org/wiki/Gauss%E2%80%93Kronrod_quadrature_formula
* </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/sample/README.md">Numerical Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gausskronrod/README.md">R<sup>1</sup> Gauss-Kronrod Quadrature Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ERFCCraig1991G7K15
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
Map<Double, BuiltInEntry> builtInTable = BuiltInEntry.Table();
System.out.println ("\t|-----------------------------------------------------||");
System.out.println ("\t| Craig 1991 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| - G7-K15 Estimate ||");
System.out.println ("\t| - Estimation Error ||");
System.out.println ("\t|-----------------------------------------------------||");
for (Map.Entry<Double, BuiltInEntry> builtInTableEntry : builtInTable.entrySet())
{
final double x = builtInTableEntry.getKey();
double erfcTable = builtInTableEntry.getValue().erfc();
R1ToR1 erfcIntegrand = new R1ToR1 (null)
{
@Override public double evaluate (
final double theta)
throws java.lang.Exception
{
if (0. == theta)
{
return 0.;
}
double sinTheta = java.lang.Math.sin (theta);
return 2. * java.lang.Math.exp (-1. * x * x / (sinTheta * sinTheta)) / Math.PI;
}
};
QuadratureEstimate quadratureEstimate = GaussKronrodQuadratureGenerator.G7K15 (
0.,
0.5 * Math.PI
).estimate (erfcIntegrand);
System.out.println (
"\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (erfcTable, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (quadratureEstimate.baseline(), 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (quadratureEstimate.error(), 1, 9, 1.) + " ||"
);
}
System.out.println ("\t|-----------------------------------------------------||");
EnvManager.TerminateEnv();
}
}