FrobeniusCovariance.java

package org.drip.function.matrix;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
 *      credit, commodity, equity, FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  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
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 *  - 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>FrobeniusCovariance</i> implements the Frobenius Co-variance of a Square Matrix, which corresponds to
 *  the Projection Shadows of Lagrange Polynomials of the Square Matrix. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Claerbout, J. F. (1985): <i>Fundamentals of Geo-physical Data Processing</i> <b>Blackwell
 *              Scientific</b>
 *      </li>
 *      <li>
 *          Horn, R. A., and C. R. Johnson (1991): <i>Topics in Matrix Analysis</i> <b>Cambridge University
 *              Press</b>
 *      </li>
 *      <li>
 *          Schwerdtfeger, A. (1938): <i>Les Fonctions de Matrices: Les Fonctions Univalentes I</i>
 *              <b>Hermann</b> Paris, France
 *      </li>
 *      <li>
 *          Sylvester, J. J. (1883): On the Equation to the Secular Inequalities in the Planetary Theory
 *              <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i> <b>16
 *              (100)</b> 267-269
 *      </li>
 *      <li>
 *          Wikipedia (2019): Sylvester Formula https://en.wikipedia.org/wiki/Sylvester%27s_formula
 *      </li>
 *  </ul>
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalSupportLibrary.md">Numerical Support Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/matrix/README.md">Linear Algebra and Matrix Utilities</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class FrobeniusCovariance
{
    private java.util.Map<java.lang.Double, org.drip.function.matrix.Square> _componentMap = null;

    /**
     * Empty FrobeniusCovariance Constructor
     */

    public FrobeniusCovariance()
    {
    }

    /**
     * Add a Frobenius Component
     * 
     * @param eigenValue The Frobenius Component EigenValue
     * @param component The Frobenius Component
     * 
     * @return TRUE - The Frobenius Component successfully added
     */

    public boolean addComponent (
        final double eigenValue,
        final org.drip.function.matrix.Square component)
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (
                eigenValue
            ) || null == component
        )
        {
            return false;
        }

        if (null == _componentMap)
        {
            _componentMap = new java.util.TreeMap<java.lang.Double, org.drip.function.matrix.Square>();
        }

        _componentMap.put (
            eigenValue,
            component
        );

        return true;
    }

    /**
     * Retrieve the Map of Frobenius Components
     * 
     * @return Map of Frobenius Components
     */

    public java.util.Map<java.lang.Double, org.drip.function.matrix.Square> componentMap()
    {
        return _componentMap;
    }
}