NewtonCotesQuadratureGenerator.java
package org.drip.numerical.integration;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* 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
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - 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>NewtonCotesQuadratureGenerator</i> generates the Array of Newton-Cotes Based Quadrature Abscissa and
* their corresponding Weights. 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/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/integration/README.md">R<sup>1</sup> R<sup>d</sup> Numerical Integration Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class NewtonCotesQuadratureGenerator
{
/**
* Generate the Newton-Cotes of Equally Spaced Quadrature over (0, +1)
*
* @param abscissaTransformer The Abscissa Transformer
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes of Equally Spaced Quadrature over (0, +1)
*/
public static final org.drip.numerical.integration.QuadratureEstimator Zero_PlusOne (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer,
final int intermediatePointCount)
{
if (0 >= intermediatePointCount)
{
return null;
}
int nodeCount = intermediatePointCount + 2;
double width = 1. / (intermediatePointCount + 1);
double[] abscissaArray = new double[nodeCount];
double[] weightArray = new double[nodeCount];
weightArray[intermediatePointCount + 1] = 0.5 * width;
abscissaArray[intermediatePointCount + 1] = 1.;
weightArray[0] = 0.5 * width;
abscissaArray[0] = 0.;
for (int intermediatePointIndex = 0; intermediatePointIndex < intermediatePointCount;
++intermediatePointIndex)
{
weightArray[intermediatePointIndex + 1] = width;
abscissaArray[intermediatePointIndex + 1] = width * (intermediatePointIndex + 1);
}
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
abscissaArray,
weightArray
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Newton-Cotes of Equally Spaced Quadrature over (-1, +1)
*
* @param abscissaTransformer The Abscissa Transformer
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes of Equally Spaced Quadrature over (1, +1)
*/
public static final org.drip.numerical.integration.QuadratureEstimator MinusOne_PlusOne (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer,
final int intermediatePointCount)
{
if (0 >= intermediatePointCount)
{
return null;
}
int nodeCount = intermediatePointCount + 2;
double[] weightArray = new double[nodeCount];
double[] abscissaArray = new double[nodeCount];
double width = 2. / (intermediatePointCount + 1);
weightArray[intermediatePointCount + 1] = 0.5 * width;
abscissaArray[intermediatePointCount + 1] = 1.;
weightArray[0] = 0.5 * width;
abscissaArray[0] = -1.;
for (int intermediatePointIndex = 0; intermediatePointIndex < intermediatePointCount;
++intermediatePointIndex)
{
weightArray[intermediatePointIndex + 1] = width;
abscissaArray[intermediatePointIndex + 1] = width * (intermediatePointIndex + 1) - 1.;
}
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
abscissaArray,
weightArray
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (0, +1)
*/
public static final org.drip.numerical.integration.QuadratureEstimator Zero_PlusOne (
final double left,
final double right,
final int intermediatePointCount)
{
return Zero_PlusOne (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleZero_PlusOne (
left,
right
),
intermediatePointCount
);
}
/**
* Generate the Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes of Equally Spaced Quadrature over (a, b) onto (-1, +1)
*/
public static final org.drip.numerical.integration.QuadratureEstimator MinusOne_PlusOne (
final double left,
final double right,
final int intermediatePointCount)
{
return MinusOne_PlusOne (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
),
intermediatePointCount
);
}
/**
* Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
*
* @param left Left Integrand Quadrature Limit
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (a, +Infinity)
*/
public static final org.drip.numerical.integration.QuadratureEstimator GaussLaguerreLeftDefinite (
final double left,
final int intermediatePointCount)
{
return Zero_PlusOne (
org.drip.numerical.integration.AbscissaTransform.GaussLaguerreLeftDefinite (left),
intermediatePointCount
);
}
/**
* Generate the Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
*
* @param right Right Integrand Quadrature Limit
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes Quadrature for the Gauss-Laguerre Left-Definite Integral over (-Infinity, a)
*/
public static final org.drip.numerical.integration.QuadratureEstimator GaussLaguerreRightDefinite (
final double right,
final int intermediatePointCount)
{
return Zero_PlusOne (
org.drip.numerical.integration.AbscissaTransform.GaussLaguerreRightDefinite (right),
intermediatePointCount
);
}
/**
* Generate the Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over
* (-Infinity, +Infinity)
*
* @param intermediatePointCount Number of Intermediate Points
*
* @return The Newton-Cotes Quadrature for the Gauss-Hermite Indefinite Integral over
* (-Infinity, +Infinity)
*/
public static final org.drip.numerical.integration.QuadratureEstimator GaussHermite (
final int intermediatePointCount)
{
return MinusOne_PlusOne (
org.drip.numerical.integration.AbscissaTransform.GaussHermite(),
intermediatePointCount
);
}
}