SylvesterInterpolantReconciler.java

package org.drip.sample.matrix;

import java.util.Map;

import org.drip.function.definition.R1ToR1;
import org.drip.function.matrix.FrobeniusCovariance;
import org.drip.function.matrix.Square;
import org.drip.numerical.common.NumberUtil;
import org.drip.numerical.eigen.EigenOutput;
import org.drip.numerical.eigen.QREigenComponentExtractor;
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
 * 
 *  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>SylvesterInterpolantReconciler</i> demonstrates the Construction and Usage of the Sylvester Matrix
 *  Interpolant. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Claerbout, J. F. (1985): <i>Fundamentals of Geo-physical Data Processing</i> <b>Blackwell
 *              Scientific</b>
 *      </li>
 *      <li>
 *          Horn, R. A., and C. R. Johnson (1991): <i>Topics in Matrix Analysis</i> <b>Cambridge University
 *              Press</b>
 *      </li>
 *      <li>
 *          Schwerdtfeger, A. (1938): <i>Les Fonctions de Matrices: Les Fonctions Univalentes I</i>
 *              <b>Hermann</b> Paris, France
 *      </li>
 *      <li>
 *          Sylvester, J. J. (1883): On the Equation to the Secular Inequalities in the Planetary Theory
 *              <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i> <b>16
 *              (100)</b> 267-269
 *      </li>
 *      <li>
 *          Wikipedia (2019): Sylvester Formula https://en.wikipedia.org/wiki/Sylvester%27s_formula
 *      </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 SylvesterInterpolantReconciler
{

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

        double[][] a =
        {
            {1, 3},
            {4, 2},
        };

        QREigenComponentExtractor qrece = new QREigenComponentExtractor (
            50,
            0.00001
        );

        EigenOutput eigenOutput = qrece.eigenize (
            a
        );

        double[] eigenValueArray = eigenOutput.eigenValueArray();

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

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

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

        System.out.println();

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

        System.out.println ("\t|              EIGEN VALUES               |");

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

        System.out.println ("\t|  " + eigenValueArray[0] + "  |  " + eigenValueArray[1]);

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

        double[][] frobeniusCovariant0 = new double[2][2];
        double[][] frobeniusCovariant1 = new double[2][2];
        frobeniusCovariant0[0][0] = (a[0][0] - eigenValueArray[1]) / (eigenValueArray[0] - eigenValueArray[1]);
        frobeniusCovariant0[1][1] = (a[1][1] - eigenValueArray[1]) / (eigenValueArray[0] - eigenValueArray[1]);
        frobeniusCovariant0[0][1] = a[0][1] / (eigenValueArray[0] - eigenValueArray[1]);
        frobeniusCovariant0[1][0] = a[1][0] / (eigenValueArray[0] - eigenValueArray[1]);
        frobeniusCovariant1[0][0] = (a[0][0] - eigenValueArray[0]) / (eigenValueArray[1] - eigenValueArray[0]);
        frobeniusCovariant1[1][1] = (a[1][1] - eigenValueArray[0]) / (eigenValueArray[1] - eigenValueArray[0]);
        frobeniusCovariant1[0][1] = a[0][1] / (eigenValueArray[1] - eigenValueArray[0]);
        frobeniusCovariant1[1][0] = a[1][0] / (eigenValueArray[1] - eigenValueArray[0]);

        System.out.println();

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

        System.out.println ("\t|          SYLVESTER RECONCILER           |");

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

        NumberUtil.PrintMatrix (
            "\t| FROBENIUS COVARIANT 0",
            frobeniusCovariant0
        );

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

        NumberUtil.PrintMatrix (
            "\t| FROBENIUS COVARIANT 1",
            frobeniusCovariant1
        );

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

        double[][] recoveredA = Matrix.Scale2D (
            frobeniusCovariant0,
            eigenValueArray[0]
        );

        double[][] recoveredA1 = Matrix.Scale2D (
            frobeniusCovariant1,
            eigenValueArray[1]
        );

        recoveredA[0][0] += recoveredA1[0][0];
        recoveredA[0][1] += recoveredA1[0][1];
        recoveredA[1][0] += recoveredA1[1][0];
        recoveredA[1][1] += recoveredA1[1][1];

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

        NumberUtil.PrintMatrix (
            "\t| RECOVERED MATRIX",
            recoveredA
        );

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

        double[][] inverseA = Matrix.Scale2D (
            frobeniusCovariant0,
            1. / eigenValueArray[0]
        );

        double[][] inverseA1 = Matrix.Scale2D (
            frobeniusCovariant1,
            1. / eigenValueArray[1]
        );

        inverseA[0][0] += inverseA1[0][0];
        inverseA[0][1] += inverseA1[0][1];
        inverseA[1][0] += inverseA1[1][0];
        inverseA[1][1] += inverseA1[1][1];

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

        NumberUtil.PrintMatrix (
            "\t| INVERSE MATRIX",
            inverseA
        );

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

        NumberUtil.PrintMatrix (
            "\t| INVERSE MATRIX",
            Matrix.Invert (
                a,
                ""
            )
        );

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

        Square aSquare = new Square (
            a
        );

        FrobeniusCovariance frobeniusCovariance = aSquare.frobeniusCovariance();

        Map<Double, Square> componentMap = frobeniusCovariance.componentMap();

        Object[] eigenValueKey = componentMap.keySet().toArray();

        frobeniusCovariant0 = componentMap.get (
            eigenValueKey[0]
        ).grid();

        frobeniusCovariant1 = frobeniusCovariance.componentMap().get (
            eigenValueKey[1]
        ).grid();

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

        System.out.println ("\t|          SYLVESTER RECONCILER           |");

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

        NumberUtil.PrintMatrix (
            "\t| FROBENIUS COVARIANT 0",
            frobeniusCovariant0
        );

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

        NumberUtil.PrintMatrix (
            "\t| FROBENIUS COVARIANT 1",
            frobeniusCovariant1
        );

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

        recoveredA = aSquare.evaluate (
            new R1ToR1 (
                null
            )
            {
                @Override public double evaluate (
                    final double x)
                    throws Exception
                {
                    return x;
                }
            }
        );

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

        NumberUtil.PrintMatrix (
            "\t| RECOVERED MATRIX",
            recoveredA
        );

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

        inverseA = aSquare.evaluate (
            new R1ToR1 (
                null
            )
            {
                @Override public double evaluate (
                    final double x)
                    throws Exception
                {
                    return 1. / x;
                }
            }
        );

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

        NumberUtil.PrintMatrix (
            "\t| INVERSE MATRIX",
            inverseA
        );

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

        EnvManager.TerminateEnv();
    }
}