GaussLegendreQuadratureGenerator.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>GaussLegendreQuadratureGenerator</i> generates the Array of Orthogonal Legendre Polynomial Gaussian
* Quadrature Based Abscissa and their corresponding Weights. 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/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 GaussLegendreQuadratureGenerator
{
/**
* Generate the One Point Gauss Legendre Quadrature over [-1, +1]
*
* @param abscissaTransformer The Abscissa Transformer
*
* @return The One Point Gauss Legendre Quadrature over [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator OnePoint (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
{
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
new double[]
{
0.000000000000000,
},
new double[]
{
2.000000000000000,
}
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Two Point Gauss Legendre Quadrature over [-1, +1]
*
* @param abscissaTransformer The Abscissa Transformer
*
* @return The Two Point Gauss Legendre Quadrature over [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator TwoPoint (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
{
double sqrt_1Over3_ = java.lang.Math.sqrt (1. / 3.);
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
new double[]
{
-sqrt_1Over3_,
sqrt_1Over3_,
},
new double[]
{
1.000000000000000,
1.000000000000000,
}
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Three Point Gauss Legendre Quadrature over [-1, +1]
*
* @param abscissaTransformer The Abscissa Transformer
*
* @return The Three Point Gauss Legendre Quadrature over [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
{
double sqrt_3Over5_ = java.lang.Math.sqrt (3. / 5.);
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
new double[]
{
-sqrt_3Over5_,
0.000000000000000,
sqrt_3Over5_,
},
new double[]
{
5. / 9.,
8. / 9.,
5. / 9.,
}
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Four Point Gauss Legendre Quadrature over [-1, +1]
*
* @param abscissaTransformer The Abscissa Transformer
*
* @return The Four Point Gauss Legendre Quadrature over [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
{
double sqrt_30_Over36 = java.lang.Math.sqrt (30.) / 36.;
double nearWeight = 0.5 + sqrt_30_Over36;
double farWeight = 0.5 - sqrt_30_Over36;
double threeOver7 = 3. / 7.;
double twoOver7Sqrt_6Over5_ = 2. / 7. * java.lang.Math.sqrt (6. / 5.);
double farNode = java.lang.Math.sqrt (threeOver7 + twoOver7Sqrt_6Over5_);
double nearNode = java.lang.Math.sqrt (threeOver7 - twoOver7Sqrt_6Over5_);
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
new double[]
{
-farNode,
-nearNode,
nearNode,
farNode,
},
new double[]
{
farWeight,
nearWeight,
nearWeight,
farWeight,
}
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Five Point Gauss Legendre Quadrature over [-1, +1]
*
* @param abscissaTransformer The Abscissa Transformer
*
* @return The Five Point Gauss Legendre Quadrature over [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
final org.drip.numerical.integration.AbscissaTransform abscissaTransformer)
{
double thirteenSqrt_70_ = 13. * java.lang.Math.sqrt (70.);
double nearWeight = (322. + thirteenSqrt_70_) / 900.;
double farWeight = (322. - thirteenSqrt_70_) / 900.;
double twoSqrt_10Over7_ = 2. * java.lang.Math.sqrt (10. / 7.);
double farNode = java.lang.Math.sqrt (5. + twoSqrt_10Over7_) / 3.;
double nearNode = java.lang.Math.sqrt (5. - twoSqrt_10Over7_) / 3.;
try
{
return new org.drip.numerical.integration.QuadratureEstimator (
abscissaTransformer,
org.drip.numerical.common.Array2D.FromArray (
new double[]
{
-farNode,
-nearNode,
0.000000000000000,
nearNode,
farNode,
},
new double[]
{
farWeight,
nearWeight,
128. / 225.,
nearWeight,
farWeight,
}
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the One Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
*
* @return The One Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator OnePoint (
final double left,
final double right)
{
return OnePoint (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
)
);
}
/**
* Generate the Two Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
*
* @return The Two Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator TwoPoint (
final double left,
final double right)
{
return TwoPoint (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
)
);
}
/**
* Generate the Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
*
* @return The Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator ThreePoint (
final double left,
final double right)
{
return ThreePoint (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
)
);
}
/**
* Generate the Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
*
* @return The Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator FourPoint (
final double left,
final double right)
{
return FourPoint (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
)
);
}
/**
* Generate the Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*
* @param left Left Integrand Quadrature Limit
* @param right Right Integrand Quadrature Limit
*
* @return The Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
*/
public static final org.drip.numerical.integration.QuadratureEstimator FivePoint (
final double left,
final double right)
{
return FivePoint (
org.drip.numerical.integration.AbscissaTransform.DisplaceAndScaleMinusOne_PlusOne (
left,
right
)
);
}
}