MultivariateRandom.java

package org.drip.sequence.functional;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, 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 main 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 Library
 *  - Numerical Optimizer Library
 *  - Machine Learning Library
 *  - Spline Builder Library
 * 
 *  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
 *  - 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>MultivariateRandom</i> contains the implementation of the objective Function dependent on Multivariate
 * Random Variables.
 * 
 * <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/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence">Sequence</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence/functional">Functional</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public abstract class MultivariateRandom extends org.drip.function.definition.RdToR1 {

    protected MultivariateRandom()
    {
        super (null);
    }

    /**
     * Compute the Target Variate Function Metrics conditional on the specified Input Non-Target Variate
     *  Parameter Sequence Off of the Target Variate Ghost Sample Sequence
     * 
     * @param adblNonTargetVariate The Non-Target Variate Parameters
     * @param iTargetVariateIndex Target Variate Index
     * @param adblTargetVariateGhostSample Target Variate Ghost Sample
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ghostTargetVariateMetrics (
        final double[] adblNonTargetVariate,
        final int iTargetVariateIndex,
        final double[] adblTargetVariateGhostSample)
    {
        if (!org.drip.function.definition.RdToR1.ValidateInput (adblNonTargetVariate) ||
            null == adblTargetVariateGhostSample)
            return null;

        int iNumNonTargetVariate = adblNonTargetVariate.length;
        int iNumTargetVariateSample = adblTargetVariateGhostSample.length;

        if (0 > iTargetVariateIndex || iTargetVariateIndex > iNumNonTargetVariate || 0 ==
            iNumTargetVariateSample)
            return null;

        double[] adblFunctionArgs = new double[iNumNonTargetVariate + 1];
        double[] adblFunctionSequence = new double[iNumTargetVariateSample];

        for (int i = 0; i < iNumNonTargetVariate; ++i) {
            if (i < iTargetVariateIndex)
                adblFunctionArgs[i] = adblNonTargetVariate[i];
            else if (i >= iTargetVariateIndex)
                adblFunctionArgs[i + 1] = adblNonTargetVariate[i];
        }

        try {
            for (int i = 0; i < iNumTargetVariateSample; ++i) {
                adblFunctionArgs[iTargetVariateIndex] = adblTargetVariateGhostSample[i];

                adblFunctionSequence[i] = evaluate (adblFunctionArgs);
            }

            return new org.drip.sequence.metrics.SingleSequenceAgnosticMetrics (adblFunctionSequence, null);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Compute the Target Variate Function Metrics conditional on the specified Input Non-Target Variate
     *  Parameter Sequence Off of the Target Variate Ghost Sample Sequence
     * 
     * @param aSSAM Array of Variate Sequence Metrics
     * @param aiNonTargetVariateSequenceIndex Array of Non-Target Variate Sequence Indexes
     * @param iTargetVariateIndex Target Variate Index
     * @param adblTargetVariateGhostSample Target Variate Ghost Sample
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ghostTargetVariateMetrics (
        final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics[] aSSAM,
        final int[] aiNonTargetVariateSequenceIndex,
        final int iTargetVariateIndex,
        final double[] adblTargetVariateGhostSample)
    {
        if (null == aSSAM || null == aiNonTargetVariateSequenceIndex || 0 > iTargetVariateIndex) return null;

        int iNumNonTargetVariate = aSSAM.length - 1;
        double[] adblNonTargetVariate = new double[iNumNonTargetVariate];

        if (0 >= iNumNonTargetVariate || iNumNonTargetVariate != aiNonTargetVariateSequenceIndex.length ||
            iTargetVariateIndex > iNumNonTargetVariate)
            return null;

        for (int i = 0; i < iNumNonTargetVariate; ++i)
            adblNonTargetVariate[i] = aSSAM[i < iTargetVariateIndex ? i : i +
                1].sequence()[aiNonTargetVariateSequenceIndex[i]];

        return ghostTargetVariateMetrics (adblNonTargetVariate, iTargetVariateIndex,
            adblTargetVariateGhostSample);
    }

    /**
     * Compute the Target Variate Function Metrics over the full Non-target Variate Empirical Distribution
     *  Off of the Target Variate Ghost Sample Sequence
     * 
     * @param aSSAM Array of Variate Sequence Metrics
     * @param iTargetVariateIndex Target Variate Index
     * @param adblTargetVariateGhostSample Target Variate Ghost Sample
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ghostTargetVariateMetrics (
        final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics[] aSSAM,
        final int iTargetVariateIndex,
        final double[] adblTargetVariateGhostSample)
    {
        if (null == aSSAM || 0 > iTargetVariateIndex) return null;

        int iTargetVariateVarianceIndex = 0;
        int iNumNonTargetVariate = aSSAM.length - 1;

        if (0 >= iNumNonTargetVariate) return null;

        org.drip.spaces.iterator.SequenceIndexIterator sii =
            org.drip.spaces.iterator.SequenceIndexIterator.Standard (iNumNonTargetVariate,
                aSSAM[0].sequence().length);

        if (null == sii) return null;

        double[] adblTargetVariateVariance = new double[sii.size()];

        int[] aiNonTargetVariateSequenceIndex = sii.first();

        while (null != aiNonTargetVariateSequenceIndex && aiNonTargetVariateSequenceIndex.length ==
            iNumNonTargetVariate) {
            org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ssamGhostConditional =
                ghostTargetVariateMetrics (aSSAM, aiNonTargetVariateSequenceIndex, iTargetVariateIndex,
                    adblTargetVariateGhostSample);

            if (null == ssamGhostConditional) return null;

            adblTargetVariateVariance[iTargetVariateVarianceIndex++] =
                ssamGhostConditional.empiricalVariance();

            aiNonTargetVariateSequenceIndex = sii.next();
        }

        try {
            return new org.drip.sequence.metrics.SingleSequenceAgnosticMetrics (adblTargetVariateVariance,
                null);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Compute the Target Variate Function Metrics Conditional on the specified Input Non-Target Variate
     *  Parameter Sequence
     * 
     * @param adblNonTargetVariate The Non-Target Variate Parameters
     * @param iTargetVariateIndex Target Variate Index
     * @param ssamTarget Target Variate Metrics
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics conditionalTargetVariateMetrics (
        final double[] adblNonTargetVariate,
        final int iTargetVariateIndex,
        final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ssamTarget)
    {
        return null == ssamTarget ? null : ghostTargetVariateMetrics (adblNonTargetVariate,
            iTargetVariateIndex, ssamTarget.sequence());
    }

    /**
     * Compute the Target Variate Function Metrics Conditional on the specified Input Non-target Variate
     *  Parameter Sequence
     * 
     * @param aSSAM Array of Variate Sequence Metrics
     * @param aiNonTargetVariateSequenceIndex Array of Non-Target Variate Sequence Indexes
     * @param iTargetVariateIndex Target Variate Index
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics conditionalTargetVariateMetrics (
        final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics[] aSSAM,
        final int[] aiNonTargetVariateSequenceIndex,
        final int iTargetVariateIndex)
    {
        if (null == aSSAM || null == aiNonTargetVariateSequenceIndex || 0 > iTargetVariateIndex) return null;

        int iNumNonTargetVariate = aSSAM.length - 1;
        double[] adblNonTargetVariate = new double[iNumNonTargetVariate];

        if (0 >= iNumNonTargetVariate || iNumNonTargetVariate != aiNonTargetVariateSequenceIndex.length ||
            iTargetVariateIndex > iNumNonTargetVariate)
            return null;

        for (int i = 0; i < iNumNonTargetVariate; ++i)
            adblNonTargetVariate[i] = aSSAM[i < iTargetVariateIndex ? i : i +
                1].sequence()[aiNonTargetVariateSequenceIndex[i]];

        return conditionalTargetVariateMetrics (adblNonTargetVariate, iTargetVariateIndex,
            aSSAM[iTargetVariateIndex]);
    }

    /**
     * Compute the Target Variate Function Metrics over the full Non-target Variate Empirical Distribution
     * 
     * @param aSSAM Array of Variate Sequence Metrics
     * @param iTargetVariateIndex Target Variate Index
     * 
     * @return The Variate-specific Function Metrics
     */

    public org.drip.sequence.metrics.SingleSequenceAgnosticMetrics unconditionalTargetVariateMetrics (
        final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics[] aSSAM,
        final int iTargetVariateIndex)
    {
        if (null == aSSAM || 0 > iTargetVariateIndex) return null;

        int iTargetVariateVarianceIndex = 0;
        int iNumNonTargetVariate = aSSAM.length - 1;

        if (0 >= iNumNonTargetVariate) return null;

        org.drip.spaces.iterator.SequenceIndexIterator sii =
            org.drip.spaces.iterator.SequenceIndexIterator.Standard (iNumNonTargetVariate,
                aSSAM[0].sequence().length);

        if (null == sii) return null;

        double[] adblTargetVariateVariance = new double[sii.size()];

        int[] aiNonTargetVariateSequenceIndex = sii.first();

        while (null != aiNonTargetVariateSequenceIndex && aiNonTargetVariateSequenceIndex.length ==
            iNumNonTargetVariate) {
            org.drip.sequence.metrics.SingleSequenceAgnosticMetrics ssamConditional =
                conditionalTargetVariateMetrics (aSSAM, aiNonTargetVariateSequenceIndex,
                    iTargetVariateIndex);

            if (null == ssamConditional) return null;

            adblTargetVariateVariance[iTargetVariateVarianceIndex++] = ssamConditional.empiricalVariance();

            aiNonTargetVariateSequenceIndex = sii.next();
        }

        try {
            return new org.drip.sequence.metrics.SingleSequenceAgnosticMetrics (adblTargetVariateVariance,
                null);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}