RayleighQuotient.java

package org.drip.sample.matrix;

import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.common.NumberUtil;
import org.drip.numerical.linearalgebra.Matrix;
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
 * 
 *  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>RayleighQuotient</i> demonstrates the Computation of an Approximate to the Eigenvalue using the
 * Rayleigh Quotient. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Wikipedia - Power Iteration (2018): https://en.wikipedia.org/wiki/Power_iteration
 *      </li>
 *      <li>
 *          Wikipedia - Rayleigh Quotient Iteration (2018):
 *              https://en.wikipedia.org/wiki/Rayleigh_quotient_iteration
 *      </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/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 RayleighQuotient
{

    private static final void EigenDump (
        final int iteration,
        final double[] eigenvector,
        final double eigenvalue)
        throws Exception
    {
        java.lang.String strDump = "\t|| Iteration => " + FormatUtil.FormatDouble (iteration, 2, 0, 1.) +
            "[" + FormatUtil.FormatDouble (eigenvalue, 3, 4, 1.) + "] => ";

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

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

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

        int iterationCount = 5;
        double eigenvalue = 200.;
        double[][] a = {
            {1., 2., 3.},
            {1., 2., 1.},
            {3., 2., 1.},
        };
        double[] eigenvector = {
            1. / Math.sqrt (3.),
            1. / Math.sqrt (3.),
            1. / Math.sqrt (3.)
        };

        NumberUtil.PrintMatrix (
            "\t|| A ",
            a
        );

        EigenDump (
            0,
            eigenvector,
            eigenvalue
        );

        int iterationIndex = 0;

        while (++iterationIndex < iterationCount)
        {
            double[][] deDiagonalized = new double[a.length][a.length];

            for (int row = 0; row < a.length; ++row)
            {
                for (int column = 0; column < a.length; ++column)
                {
                    deDiagonalized[row][column] = a[row][column];

                    if (row == column)
                    {
                        deDiagonalized[row][column] -= eigenvalue;
                    }
                }
            }

            eigenvector = Matrix.Normalize (
                Matrix.Product (
                    Matrix.InvertUsingGaussianElimination (deDiagonalized),
                    eigenvector
                )
            );

            eigenvalue = Matrix.DotProduct (
                eigenvector,
                Matrix.Product (
                    a,
                    eigenvector
                )
            );

            EigenDump (
                iterationIndex,
                eigenvector,
                eigenvalue
            );
        }

        EnvManager.TerminateEnv();
    }
}