PillaiSpecialChiSquare.java

package org.drip.sample.randomdiscrete;

import org.drip.measure.discrete.SequenceGenerator;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

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

/*!
 * Copyright (C) 2019 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>PillaiSpecialChiSquare</i> demonstrates Generation of Pillai (2016) Special Chi-Squared R<sup>1</sup>
 * Random Numbers with different Degrees of Freedom.
 *
 * <br><br>
 *  <ul>
 *      <li>
 *          Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
 *              Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
 *              (1)</b> 19-30
 *      </li>
 *      <li>
 *          Chi-Squared Distribution (2019): Chi-Squared Function
 *              https://en.wikipedia.org/wiki/Chi-squared_distribution
 *      </li>
 *      <li>
 *          Johnson, N. L., S. Klotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
 *              <b>1</b> 2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
 *      </li>
 *      <li>
 *          Lancaster, H, O. (1969): <i>The Chi-Squared Distribution</i> <b>Wiley</b>
 *      </li>
 *      <li>
 *          Pillai, N. S. (1026): An Unexpected Encounter with Cauchy and Levy <i>Annals of Statistics</i>
 *              <b>44 (5)</b> 2089-2097
 *      </li>
 *  </ul>
 * 
 *  <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/NumericalOptimizerLibrary.md">Numerical Optimizer Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure">Measure</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/discrete">Discrete</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class PillaiSpecialChiSquare
{

    private static final void DisplayStream (
        final double[][] covarianceMatrix,
        final double[] weightArray)
        throws Exception
    {
        double[] randomArray = SequenceGenerator.PillaiSpecialChiSquare (
            200,
            covarianceMatrix,
            weightArray
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------------------||");

        for (int row = 0; row < 20; ++row)
        {
            String rowDump = "\t|";

            for (int column = 0; column < 10; ++column)
            {
                rowDump = rowDump + FormatUtil.FormatDouble (
                    randomArray[row * 10 + column], 2, 4, 1.
                ) + " |";
            }

            System.out.println (rowDump + "|");
        }

        System.out.println ("\t|---------------------------------------------------------------------------------------------------||");

        System.out.println();
    }

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        double[][] covarianceMatrix =
        {
            {1.00, 0.90, 0.10},
            {0.90, 1.00, 0.50},
            {0.10, 0.50, 1.00},
        };
        double[] weightArray =
        {
            0.2,
            0.3,
            0.5,
        };

        DisplayStream (
            covarianceMatrix,
            weightArray
        );

        EnvManager.TerminateEnv();
    }
}