CovarianceEllipsoidMultivariate.java

package org.drip.function.rdtor1;

/*
 * -*- 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>CovarianceEllipsoidMultivariate</i> implements a R<sup>d</sup> To R<sup>1</sup> Co-variance Estimate of
 * the specified Distribution.
 *
 *  <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/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/rdtor1/README.md">Built-in R<sup>d</sup> To R<sup>1</sup> Functions</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class CovarianceEllipsoidMultivariate extends org.drip.function.definition.RdToR1 {
    private double[][] _aadblCovarianceMatrix = null;

    /**
     * CovarianceEllipsoidMultivariate Constructor
     * 
     * @param aadblCovarianceMatrix The Covariance Matrix
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public CovarianceEllipsoidMultivariate (
        final double[][] aadblCovarianceMatrix)
        throws java.lang.Exception
    {
        super (null);

        if (null == (_aadblCovarianceMatrix = aadblCovarianceMatrix))
            throw new java.lang.Exception ("CovarianceEllipsoidMultivariate Constructor => Invalid Inputs");

        int iSize = _aadblCovarianceMatrix.length;

        if (0 == iSize)
            throw new java.lang.Exception ("CovarianceEllipsoidMultivariate Constructor => Invalid Inputs");

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

    /**
     * Retrieve the Input Variate Dimension
     * 
     * @return The Input Variate Dimension
     */

    public int dimension()
    {
        return _aadblCovarianceMatrix.length;
    }

    /**
     * Retrieve the Co-variance Matrix
     * 
     * @return The Co-variance Matrix
     */

    public double[][] covariance()
    {
        return _aadblCovarianceMatrix;
    }

    @Override public double evaluate (
        final double[] adblVariate)
        throws java.lang.Exception
    {
        if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate))
            throw new java.lang.Exception ("CovarianceEllipsoidMultivariate::evaluate => Invalid Inputs");

        double dblCovariance = 0.;
        int iDimension = adblVariate.length;

        if (iDimension != dimension())
            throw new java.lang.Exception ("CovarianceEllipsoidMultivariate::evaluate => Invalid Inputs");

        for (int i = 0; i < iDimension; ++i) {
            for (int j = 0; j < iDimension; ++j)
                dblCovariance += adblVariate[i] * _aadblCovarianceMatrix[i][j] * adblVariate[j];
        }

        return dblCovariance;
    }

    @Override public double[] jacobian (
        final double[] adblVariate)
    {
        if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate)) return null;

        int iDimension = adblVariate.length;
        double[] adblJacobian = new double[iDimension];

        if (iDimension != dimension()) return null;

        for (int i = 0; i < iDimension; ++i) {
            adblJacobian[i] = 0.;

            for (int j = 0; j < iDimension; ++j)
                adblJacobian[i] += 2. * _aadblCovarianceMatrix[i][j] * adblVariate[j];
        }

        return adblJacobian;
    }

    @Override public double[][] hessian (
        final double[] adblVariate)
    {
        int iDimension = dimension();

        double[][] aadblHessian = new double[iDimension][iDimension];

        for (int i = 0; i < iDimension; ++i) {
            for (int j = 0; j < iDimension; ++j)
                aadblHessian[i][j] += 2. * _aadblCovarianceMatrix[i][j];
        }

        return aadblHessian;
    }
}