ERFCCraig1991.java
package org.drip.sample.newtoncotes;
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.NewtonCotesQuadratureGenerator;
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>ERFCCraig1991</i> computes the R<sup>1</sup> Numerical Estimate of the erf Integrand using Newton-Cotes
* Grids. The References are:
*
* <br><br>
* <ul>
* <li>
* Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): <i>Frank-Wolfe Bayesian
* Quadrature: Probabilistic Integration with Theoretical Guarantees</i> <b>arXiv</b>
* </li>
* <li>
* Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): <i>Computer Methods for Mathematical
* Computation</i> <b>Prentice Hall</b> Englewood Cliffs NJ
* </li>
* <li>
* Leader, J. J. (2004): <i>Numerical Analysis and Scientific Computation</i> <b>Addison Wesley</b>
* </li>
* <li>
* Stoer, J., and R. Bulirsch (1980): <i>Introduction to Numerical Analysis</i>
* <b>Springer-Verlag</b> New York
* </li>
* <li>
* Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration
* </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">Sample</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/newtoncotes/README.md">R<sup>1</sup> Newton-Cotes Quadrature Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ERFCCraig1991
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int nodeCount10 = 10;
int nodeCount50 = 50;
int nodeCount100 = 100;
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| - Newton Cotes Estimate (10 Nodes) ||");
System.out.println ("\t| - Newton Cotes Estimate (50 Nodes) ||");
System.out.println ("\t| - Newton Cotes Estimate (100 Nodes) ||");
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;
}
};
double erfcEstimate10 = NewtonCotesQuadratureGenerator.Zero_PlusOne (
0.,
0.5 * Math.PI,
nodeCount10
).integrate (erfcIntegrand);
double erfcEstimate50 = NewtonCotesQuadratureGenerator.Zero_PlusOne (
0.,
0.5 * Math.PI,
nodeCount50
).integrate (erfcIntegrand);
double erfcEstimate100 = NewtonCotesQuadratureGenerator.Zero_PlusOne (
0.,
0.5 * Math.PI,
nodeCount100
).integrate (erfcIntegrand);
System.out.println (
"\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (erfcTable, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfcEstimate10, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfcEstimate50, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfcEstimate100, 1, 9, 1.) + " ||"
);
}
System.out.println ("\t|--------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}