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
* - 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>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;
}
}