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);
- }
- };
- }
- }