ChebyshevCoefficientMatrix.java

package org.drip.specialfunction.lanczos;

/*
 * -*- 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>ChebyshevCoefficientMatrix</i> holds the Chebyshev Polynomial Coefficient Matrix Entries. The
 * References are:
 * 
 * <br><br>
 * 	<ul>
 * 		<li>
 * 			Godfrey, P. (2001): Lanczos Implementation of the Gamma Function
 * 				http://www.numericana.com/answer/info/godfrey.htm
 * 		</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>
 * 			Pugh, G. R. (2004): <i>An Analysis of the Lanczos Gamma Approximation</i> Ph. D. <b>University of
 * 				British Columbia</b>
 * 		</li>
 * 		<li>
 * 			Toth V. T. (2016): Programmable Calculators – The Gamma Function
 * 				http://www.rskey.org/CMS/index.php/the-library/11
 * 		</li>
 * 		<li>
 * 			Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation
 * 		</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/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
 *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
 *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/lanczos/README.md">Lanczos Scheme for Gamma Estimate</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ChebyshevCoefficientMatrix
{

	/**
	 * Generate a n X n Chebyshev Coefficient Polynomial Matrix
	 * 
	 * @param size Size of the Matrix
	 * 
	 * @return The n X n Chebyshev Coefficient Polynomial Matrix
	 */

	public static final double[][] Rollout (
		final int size)
	{
		if (0 > size)
		{
			return null;
		}

		double[][] coefficientMatrix = new double[size + 1][size + 1];

		for (int indexJ = 0; indexJ <= size; ++indexJ)
		{
			for (int indexI = 0; indexI <= size; ++indexI)
			{
				coefficientMatrix[indexI][indexJ] = 0.;
			}
		}

		coefficientMatrix[0][0] = 1.;

		if (0 == size)
		{
			return coefficientMatrix;
		}

		coefficientMatrix[1][1] = 1.;

		if (1 == size)
		{
			return coefficientMatrix;
		}

		for (int index = 2; index <= size; ++index)
		{
			coefficientMatrix[index][0] = -1. * coefficientMatrix[index - 2][0];
			coefficientMatrix[index][index] = 2. * coefficientMatrix[index - 1][index - 1];
		}

		for (int indexJ = 1; indexJ <= size; ++indexJ)
		{
			for (int indexI = indexJ + 1; indexI <= size; ++indexI)
			{
				coefficientMatrix[indexI][indexJ] = 2. * coefficientMatrix[indexI - 1][indexJ - 1] -
					coefficientMatrix[indexI - 2][indexJ];
			}
		}

		return coefficientMatrix;
	}
}