Eigenization.java

package org.drip.sample.matrix;

import org.drip.numerical.common.*;
import org.drip.numerical.eigen.*;
import org.drip.service.env.EnvManager;

/*
 * -*- 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
 * Copyright (C) 2014 Lakshmi Krishnamurthy
 * Copyright (C) 2013 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, 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 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
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  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>Eigenization</i> demonstrates how to generate the eigenvalue and eigenvector for the Input Matrix.
 *  
 * <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/NumericalSupportLibrary.md">Numerical Support Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/matrix/README.md">Linear Algebra and Matrix Utilities</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class Eigenization {

    private static final void EigenRun (
        final QREigenComponentExtractor qrece)
    {
        double dblCorr1 = 0.5 * Math.random();

        double dblCorr2 = 0.5 * Math.random();

        double[][] aadblA = {
            {     1.0, dblCorr1,      0.0},
            {dblCorr1,      1.0, dblCorr2},
            {     0.0, dblCorr2,      1.0}
        };

        EigenOutput eo = qrece.eigenize (aadblA);

        if (null == eo) return;

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

        System.out.println (
            "\t|-----------" +
            FormatUtil.FormatDouble (dblCorr1, 1, 4, 1.) + " ||| " +
            FormatUtil.FormatDouble (dblCorr2, 1, 4, 1.) + " ---------|"
        );

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

        for (int i = 0; i < aadblA.length; ++i) {
            java.lang.String strDump = "\t[" + FormatUtil.FormatDouble (eo.eigenValueArray()[i], 1, 4, 1.) + "] => ";

            for (int j = 0; j < aadblA.length; ++j)
                strDump += FormatUtil.FormatDouble (eo.eigenVectorArray()[i][j], 1, 4, 1.) + " | ";

            System.out.println (strDump);
        }

        EigenComponent ec = qrece.principalComponent (aadblA);

        double[] adblEigenvector = ec.eigenVector();

        java.lang.String strDump = "[" + FormatUtil.FormatDouble (ec.eigenValue(), 1, 4, 1.) + "] => ";

        for (int i = 0; i < adblEigenvector.length; ++i)
            strDump += FormatUtil.FormatDouble (adblEigenvector[i], 1, 4, 1.) + " | ";

        System.out.println ("\t" + strDump);

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

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

        QREigenComponentExtractor qrece = new QREigenComponentExtractor (
            50,
            0.00001
        );

        int iNumRun = 10;

        for (int iRun = 0; iRun < iNumRun; ++iRun)
            EigenRun (qrece);

        EnvManager.TerminateEnv();
    }
}