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;
    }
}