WeightFunctionBuilder.java
package org.drip.numerical.quadrature;
/*
* -*- 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>WeightFunctionBuilder</i> builds the Weight Function associated with Different Kinds of Orthogonal
* Basis Polynomials. 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/quadrature/README.md">R<sup>1</sup> Gaussian Integration Quadrature Schemes</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class WeightFunctionBuilder
{
/**
* Generate the Legendre Polynomial Weight Function
*
* @return The Legendre Polynomial Weight Function
*/
public static final org.drip.function.definition.R1ToR1 Legendre()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
return 1.;
}
};
}
/**
* Generate the Jacobi Polynomial Weight Function
*
* @param alpha Jacobi Alpha
* @param beta Jacobi Beta
*
* @return The Jacobi Polynomial Weight Function
*/
public static final org.drip.function.definition.R1ToR1 Jacobi (
final double alpha,
final double beta)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (alpha) || -1. >= alpha || -1. >= beta)
{
return null;
}
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::Jacobi::evaluate => Invalid Inputs");
}
return java.lang.Math.pow (
1. - x,
alpha
) * java.lang.Math.pow (
1. + x,
beta
) * java.lang.Math.exp (-1. * x);
}
};
}
/**
* Generate the Chebyshev Polynomial (First-Kind) Weight Function
*
* @return The Chebyshev Polynomial (First-Kind) Weight Function
*/
public static final org.drip.function.definition.R1ToR1 ChebyshevFirstKind()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::ChebyshevFirstKind::evaluate => Invalid Inputs");
}
return 1. / java.lang.Math.sqrt (1. - x * x);
}
};
}
/**
* Generate the Chebyshev Polynomial (Second-Kind) Weight Function
*
* @return The Chebyshev Polynomial (Second-Kind) Weight Function
*/
public static final org.drip.function.definition.R1ToR1 ChebyshevSecondKind()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::ChebyshevSecondKind::evaluate => Invalid Inputs");
}
return java.lang.Math.sqrt (1. - x * x);
}
};
}
/**
* Generate the Laguerre Polynomial Weight Function
*
* @return The Laguerre Polynomial Weight Function
*/
public static final org.drip.function.definition.R1ToR1 Laguerre()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::Laguerre::evaluate => Invalid Inputs");
}
return java.lang.Math.exp (-1. * x);
}
};
}
/**
* Generate the Generalized Laguerre Polynomial Weight Function
*
* @param alpha Generalized Laguerre Alpha
*
* @return The Generalized Laguerre Polynomial Weight Function
*/
public static final org.drip.function.definition.R1ToR1 GeneralizedLaguerre (
final double alpha)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (alpha) || -1. >= alpha)
{
return null;
}
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::GeneralizedLaguerre::evaluate => Invalid Inputs");
}
return java.lang.Math.pow (
x,
alpha
) * java.lang.Math.exp (-1. * x);
}
};
}
/**
* Generate the Hermite Polynomial Weight Function
*
* @return The Hermite Polynomial Weight Function
*/
public static final org.drip.function.definition.R1ToR1 Hermite()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("WeightFunctionBuilder::Hermite::evaluate => Invalid Inputs");
}
return java.lang.Math.exp (-1. * x * x);
}
};
}
}