R1MultivariateNormalConvolutionEngine.java

package org.drip.measure.bayesian;

/*
 * -*- 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>R1NormalConvolutionEngine</i> implements the Engine that generates the Joint/Posterior Distribution
 *  from the Prior and the Conditional Joint R<sup>1</sup> Multivariate Normal Distributions.
 *
 *  <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/bayesian/README.md">Prior, Conditional, Posterior Theil Bayesian</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class R1MultivariateNormalConvolutionEngine implements org.drip.measure.bayesian.R1MultivariateConvolutionEngine {

    /**
     * Empty R1MultivariateNormalConvolutionEngine Construction
     */

    public R1MultivariateNormalConvolutionEngine()
    {
    }

    @Override public org.drip.measure.bayesian.R1MultivariateConvolutionMetrics process (
        final org.drip.measure.continuous.R1Multivariate r1mPrior,
        final org.drip.measure.continuous.R1Multivariate r1mUnconditional,
        final org.drip.measure.continuous.R1Multivariate r1mConditional)
    {
        if (null == r1mPrior || !(r1mPrior instanceof org.drip.measure.gaussian.R1MultivariateNormal) || null
            == r1mConditional || !(r1mConditional instanceof org.drip.measure.gaussian.R1MultivariateNormal)
                || null == r1mUnconditional || !(r1mUnconditional instanceof
                    org.drip.measure.gaussian.R1MultivariateNormal))
            return null;

        org.drip.measure.gaussian.R1MultivariateNormal r1mnPrior =
            (org.drip.measure.gaussian.R1MultivariateNormal) r1mPrior;
        org.drip.measure.gaussian.R1MultivariateNormal r1mnConditional =
            (org.drip.measure.gaussian.R1MultivariateNormal) r1mConditional;
        org.drip.measure.gaussian.R1MultivariateNormal r1mnUnconditional =
            (org.drip.measure.gaussian.R1MultivariateNormal) r1mUnconditional;

        double[][] aadblPriorPrecision = r1mnPrior.covariance().precisionMatrix();

        double[][] aadblConditionalPrecision = r1mnConditional.covariance().precisionMatrix();

        int iNumVariate = aadblConditionalPrecision.length;
        double[] adblJointMean = new double[iNumVariate];
        double[][] aadblJointPrecision = new double[iNumVariate][iNumVariate];
        double[][] aadblPosteriorCovariance = new double[iNumVariate][iNumVariate];

        if (aadblPriorPrecision.length != iNumVariate) return null;

        double[] adblPrecisionWeightedPriorMean = org.drip.numerical.linearalgebra.Matrix.Product
            (aadblPriorPrecision, r1mnPrior.mean());

        if (null == adblPrecisionWeightedPriorMean) return null;

        double[] adblPrecisionWeightedConditionalMean = org.drip.numerical.linearalgebra.Matrix.Product
            (aadblConditionalPrecision, r1mnConditional.mean());

        if (null == adblPrecisionWeightedConditionalMean) return null;

        for (int i = 0; i < iNumVariate; ++i) {
            adblJointMean[i] = adblPrecisionWeightedPriorMean[i] + adblPrecisionWeightedConditionalMean[i];

            for (int j = 0; j < iNumVariate; ++j)
                aadblJointPrecision[i][j] = aadblPriorPrecision[i][j] + aadblConditionalPrecision[i][j];
        }

        double[][] aadblJointCovariance = org.drip.numerical.linearalgebra.Matrix.InvertUsingGaussianElimination
            (aadblJointPrecision);

        double[] adblJointPosteriorMean = org.drip.numerical.linearalgebra.Matrix.Product (aadblJointCovariance,
            adblJointMean);

        double[][] aadblUnconditionalCovariance = r1mnUnconditional.covariance().covarianceMatrix();

        org.drip.measure.continuous.MultivariateMeta meta = r1mnPrior.meta();

        for (int i = 0; i < iNumVariate; ++i) {
            for (int j = 0; j < iNumVariate; ++j)
                aadblPosteriorCovariance[i][j] = aadblJointCovariance[i][j] +
                    aadblUnconditionalCovariance[i][j];
        }

        try {
            return new org.drip.measure.bayesian.R1MultivariateConvolutionMetrics (r1mPrior, r1mUnconditional,
                r1mConditional, new org.drip.measure.gaussian.R1MultivariateNormal (meta,
                    adblJointPosteriorMean, new org.drip.measure.gaussian.Covariance (aadblJointCovariance)),
                        new org.drip.measure.gaussian.R1MultivariateNormal (meta, adblJointPosteriorMean, new
                            org.drip.measure.gaussian.Covariance (aadblPosteriorCovariance)));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}