Covariance.java

package org.drip.measure.gaussian;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 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>Covariance</i> holds the Standard Covariance Matrix, and provides functions to manipulate it.
 *
 *  <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/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class Covariance {
    private double[][] _aadblPrecision = null;
    private double[][] _aadblCovariance = null;

    /**
     * Covariance Constructor
     * 
     * @param aadblCovariance Double Array of the Covariance Matrix
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public Covariance (
        final double[][] aadblCovariance)
        throws java.lang.Exception
    {
        if (null == (_aadblCovariance = aadblCovariance))
            throw new java.lang.Exception ("Covariance Constructor => Invalid Inputs!");

        int iNumVariate = _aadblCovariance.length;

        if (0 == iNumVariate)
            throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");

        for (int i = 0; i < iNumVariate; ++i) {
            if (null == _aadblCovariance[i] || iNumVariate != _aadblCovariance[i].length ||
                !org.drip.numerical.common.NumberUtil.IsValid (_aadblCovariance[i]))
                throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
        }

        if (null == (_aadblPrecision = org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination
            (_aadblCovariance)))
            throw new java.lang.Exception ("R1MultivariateNormal Constructor => Invalid Inputs!");
    }

    /**
     * Retrieve the Number of Variates
     * 
     * @return The Number of Variates
     */

    public int numVariate()
    {
        return _aadblCovariance.length;
    }

    /**
     * Retrieve the Covariance Matrix
     * 
     * @return The Covariance Matrix
     */

    public double[][] covarianceMatrix()
    {
        return _aadblCovariance;
    }

    /**
     * Retrieve the Precision Matrix
     * 
     * @return The Precision Matrix
     */

    public double[][] precisionMatrix()
    {
        return _aadblPrecision;
    }

    /**
     * Retrieve the Variance Array
     * 
     * @return The Variance Array
     */

    public double[] variance()
    {
        int iNumVariate = _aadblCovariance.length;
        double[] adblVariance = new double[iNumVariate];

        for (int i = 0; i < iNumVariate; ++i)
            adblVariance[i] = _aadblCovariance[i][i];

        return adblVariance;
    }

    /**
     * Retrieve the Volatility Array
     * 
     * @return The Volatility Array
     */

    public double[] volatility()
    {
        int iNumVariate = _aadblCovariance.length;
        double[] adblVolatility = new double[iNumVariate];

        for (int i = 0; i < iNumVariate; ++i)
            adblVolatility[i] = java.lang.Math.sqrt (_aadblCovariance[i][i]);

        return adblVolatility;
    }

    /**
     * Retrieve the Correlation Matrix
     * 
     * @return The Correlation Matrix
     */

    public double[][] correlationMatrix()
    {
        int iNumVariate = _aadblCovariance.length;
        double[][] aadblCorrelation = new double[iNumVariate][iNumVariate];

        double[] adblVolatility = volatility();

        for (int i = 0; i < iNumVariate; ++i) {
            for (int j = 0; j < iNumVariate; ++j)
                aadblCorrelation[i][j] = _aadblCovariance[i][j] / (adblVolatility[i] * adblVolatility[j]);
        }

        return aadblCorrelation;
    }
}