MultivariateMoments.java

package org.drip.measure.statistics;

/*
 * -*- 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>MultivariateMoments</i> generates and holds the Specified Multivariate Series Mean, Co-variance, and
 * other selected Moments.
 *
 *  <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/statistics/README.md">R<sup>1</sup> R<sup>d</sup> Thin Thick Moments</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class MultivariateMoments {
    private org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double> _mapMean = new
        org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double>();

    private org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double> _mapCovariance = new
        org.drip.analytics.support.CaseInsensitiveHashMap<java.lang.Double>();

    /**
     * Generate the MultivariateMetrics Instance from the Series Realizations provided
     * 
     * @param astrVariateName Array of Variate Name Headers
     * @param aadblVariate Array of Variate Realization Arrays
     * 
     * @return The MultivariateMetrics Instance
     */

    public static final MultivariateMoments Standard (
        final java.lang.String[] astrVariateName,
        final double[][] aadblVariate)
    {
        if (null == astrVariateName || null == aadblVariate) return null;

        int iNumVariate = astrVariateName.length;
        double[] adblMean = new double[iNumVariate];

        if (0 == iNumVariate || iNumVariate != aadblVariate.length) return null;

        int iNumSample = aadblVariate[0].length;

        if (0 == iNumSample) return null;

        MultivariateMoments mvm = new MultivariateMoments();

        for (int i = 0; i < iNumVariate; ++i) {
            adblMean[i] = 0.;
            double[] adblVariateSample = aadblVariate[i];

            if (null == adblVariateSample || adblVariateSample.length != iNumSample) return null;

            for (int k = 0; k < iNumSample; ++k) {
                if (!org.drip.numerical.common.NumberUtil.IsValid (adblVariateSample[k])) return null;

                adblMean[i] += adblVariateSample[k];
            }

            if (!mvm.addMean (astrVariateName[i], adblMean[i] /= iNumSample)) return null;
        }

        for (int i = 0; i < iNumVariate; ++i) {
            for (int j = 0; j < iNumVariate; ++j) {
                double dblCovariance = 0.;

                for (int k = 0; k < iNumSample; ++k)
                    dblCovariance += (aadblVariate[i][k] - adblMean[i]) * (aadblVariate[j][k] - adblMean[j]);

                if (!mvm.addCovariance (astrVariateName[i], astrVariateName[j], dblCovariance / iNumSample))
                    return null;
            }
        }

        return mvm;
    }

    /**
     * Generate the MultivariateMetrics Instance from the Specified Mean and Co-variance Inputs
     * 
     * @param astrVariateName Array of Variate Name Headers
     * @param adblMean Array of Variate Means
     * @param aadblCovariance Double Array of the Variate Co-variance
     * 
     * @return The MultivariateMetrics Instance
     */

    public static final MultivariateMoments Standard (
        final java.lang.String[] astrVariateName,
        final double[] adblMean,
        final double[][] aadblCovariance)
    {
        if (null == astrVariateName || null == adblMean || null == aadblCovariance) return null;

        int iNumVariate = astrVariateName.length;

        if (0 == iNumVariate || iNumVariate != adblMean.length || iNumVariate != aadblCovariance.length ||
            null == aadblCovariance[0] || iNumVariate != aadblCovariance[0].length)
            return null;

        MultivariateMoments mvm = new MultivariateMoments();

        for (int i = 0; i < iNumVariate; ++i) {
            if (!mvm.addMean (astrVariateName[i], adblMean[i])) return null;
        }

        for (int i = 0; i < iNumVariate; ++i) {
            for (int j = 0; j < iNumVariate; ++j) {
                if (!mvm.addCovariance (astrVariateName[i], astrVariateName[j], aadblCovariance[i][j]))
                    return null;
            }
        }

        return mvm;
    }

    protected MultivariateMoments()
    {
    }

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

    public int numVariate()
    {
        return _mapMean.size();
    }

    /**
     * Retrieve the Variates for which the Metrics are available
     * 
     * @return The Set of Variates
     */

    public java.util.Set<java.lang.String> variateList()
    {
        return _mapMean.keySet();
    }

    /**
     * Add the Mean for the Named Variate
     * 
     * @param strVariateName The Named Variate
     * @param dblMean The Variate Mean
     * 
     * @return TRUE - The Variate Mean successfully added
     */

    public boolean addMean (
        final java.lang.String strVariateName,
        final double dblMean)
    {
        if (null == strVariateName || strVariateName.isEmpty() || !org.drip.numerical.common.NumberUtil.IsValid
            (dblMean))
            return false;

        _mapMean.put (strVariateName, dblMean);

        return true;
    }

    /**
     * Retrieve the Mean of the Named Variate
     * 
     * @param strVariateName The Named Variate
     * 
     * @return Mean of the Named Variate
     * 
     * @throws java.lang.Exception Thrown if the Named Variate Mean cannot be retrieved
     */

    public double mean (
        final java.lang.String strVariateName)
        throws java.lang.Exception
    {
        if (null == strVariateName || strVariateName.isEmpty() || !_mapMean.containsKey (strVariateName))
            throw new java.lang.Exception ("MultivariateMetrics::mean => Invalid Inputs");

        return _mapMean.get (strVariateName);
    }

    /**
     * Add the Co-variance for the Named Variate Pair
     * 
     * @param strVariate1Name The Named Variate #1
     * @param strVariate2Name The Named Variate #2
     * @param dblCovariance The Variate Mean
     * 
     * @return TRUE - The Variate Pair Co-variance successfully added
     */

    public boolean addCovariance (
        final java.lang.String strVariate1Name,
        final java.lang.String strVariate2Name,
        final double dblCovariance)
    {
        if (null == strVariate1Name || strVariate1Name.isEmpty() || null == strVariate2Name ||
            strVariate2Name.isEmpty() || !org.drip.numerical.common.NumberUtil.IsValid (dblCovariance))
            return false;

        _mapCovariance.put (strVariate1Name + "@#" + strVariate2Name, dblCovariance);

        _mapCovariance.put (strVariate2Name + "@#" + strVariate1Name, dblCovariance);

        return true;
    }

    /**
     * Retrieve the Variance of the Named Variate
     * 
     * @param strVariateName The Named Variate
     * 
     * @return Variance of the Named Variate
     * 
     * @throws java.lang.Exception Thrown if the Named Variate Variance cannot be retrieved
     */

    public double variance (
        final java.lang.String strVariateName)
        throws java.lang.Exception
    {
        if (null == strVariateName || strVariateName.isEmpty())
            throw new java.lang.Exception ("MultivariateMetrics::variance => Invalid Inputs");

        java.lang.String strVarianceEntry = strVariateName + "@#" + strVariateName;

        if (!_mapCovariance.containsKey (strVarianceEntry))
            throw new java.lang.Exception ("MultivariateMetrics::variance => Invalid Inputs");

        return _mapCovariance.get (strVarianceEntry);
    }

    /**
     * Retrieve the Co-variance of the Named Variate Pair
     * 
     * @param strVariate1Name The Named Variate #1
     * @param strVariate2Name The Named Variate #2
     * 
     * @return Co-variance of the Named Variate Pair
     * 
     * @throws java.lang.Exception Thrown if the Named Variate Co-variance cannot be retrieved
     */

    public double covariance (
        final java.lang.String strVariate1Name,
        final java.lang.String strVariate2Name)
        throws java.lang.Exception
    {
        if (null == strVariate1Name || strVariate1Name.isEmpty() || null == strVariate2Name ||
            strVariate2Name.isEmpty())
            throw new java.lang.Exception ("MultivariateMetrics::covariance => Invalid Inputs");

        java.lang.String strCovarianceEntry = strVariate1Name + "@#" + strVariate2Name;

        if (!_mapCovariance.containsKey (strCovarianceEntry))
            throw new java.lang.Exception ("MultivariateMetrics::coariance => Invalid Inputs");

        return _mapCovariance.get (strCovarianceEntry);
    }

    /**
     * Retrieve the Correlation between the Named Variate Pair
     * 
     * @param strVariate1Name The Named Variate #1
     * @param strVariate2Name The Named Variate #2
     * 
     * @return Correlation between the Named Variate Pair
     * 
     * @throws java.lang.Exception Thrown if the Named Variate Correlation cannot be retrieved
     */

    public double correlation (
        final java.lang.String strVariate1Name,
        final java.lang.String strVariate2Name)
        throws java.lang.Exception
    {
        return covariance (strVariate1Name, strVariate2Name) / java.lang.Math.sqrt (variance
            (strVariate1Name) * variance (strVariate2Name));
    }
}