CubicPolyGaussLegendre.java
package org.drip.sample.gaussquadrature;
import org.drip.function.definition.R1ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.integration.GaussLegendreQuadratureGenerator;
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>CubicPolyGaussLegendre</i> computes the R<sup>1</sup> Numerical Estimate of the Cubic Polynomial
* Integrand using the Gauss-Legendre Integration Quadrature Scheme. 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>
* Gil, A., J. Segura, and N. M. Temme (2007): <i>Numerical Methods for Special Functions</i>
* <b>Society for Industrial and Applied Mathematics</b> Philadelphia
* </li>
* <li>
* Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
* The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
* </li>
* <li>
* Stoer, J., and R. Bulirsch (2002): <i>Introduction to Numerical Analysis 3rd Edition</i>
* <b>Springer</b>
* </li>
* <li>
* Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature
* </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/numerical/README.md">Numerical Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/gaussquadrature/README.md">R<sup>1</sup> Gauss-Legendre Gauss-Lobatto Quadratures</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class CubicPolyGaussLegendre
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
R1ToR1 cubicPolyIntegrand = new R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws Exception
{
return 7. * x * x * x - 8. * x * x - 3. * x + 3;
}
};
double[] xArray =
{
-0.90,
-0.80,
-0.70,
-0.60,
-0.50,
-0.40,
-0.30,
-0.20,
-0.10,
0.00,
0.10,
0.20,
0.30,
0.40,
0.50,
0.60,
0.70,
0.80,
0.90,
1.00,
};
System.out.println ("\t|-----------------------------------------------------------------------------------||");
System.out.println ("\t| Cubic Polynomial Estimate ||");
System.out.println ("\t|-----------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - x ||");
System.out.println ("\t| - 5P Estimate ||");
System.out.println ("\t| - 4P Estimate ||");
System.out.println ("\t| - 3P Estimate ||");
System.out.println ("\t| - 2P Estimate ||");
System.out.println ("\t| - 1P Estimate ||");
System.out.println ("\t|-----------------------------------------------------------------------------------||");
for (double x : xArray)
{
double erfEstimate5P = GaussLegendreQuadratureGenerator.FivePoint (
-1.,
x
).integrate (cubicPolyIntegrand);
double erfEstimate4P = GaussLegendreQuadratureGenerator.FourPoint (
-1.,
x
).integrate (cubicPolyIntegrand);
double erfEstimate3P = GaussLegendreQuadratureGenerator.ThreePoint (
-1.,
x
).integrate (cubicPolyIntegrand);
double erfEstimate2P = GaussLegendreQuadratureGenerator.TwoPoint (
-1.,
x
).integrate (cubicPolyIntegrand);
double erfEstimate1P = GaussLegendreQuadratureGenerator.OnePoint (
-1.,
x
).integrate (cubicPolyIntegrand);
System.out.println (
"\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (erfEstimate5P, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfEstimate4P, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfEstimate3P, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfEstimate2P, 1, 9, 1.) + " | " +
FormatUtil.FormatDouble (erfEstimate1P, 1, 9, 1.) + " ||"
);
}
System.out.println ("\t|-----------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}