ConstrainedCovarianceEllipsoid.java

package org.drip.sample.rdtor1;

import org.drip.function.definition.RdToR1;
import org.drip.function.rdtor1.*;
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) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * ConstrainedCovarianceEllipsoid demonstrates the Construction and Usage of a Co-variance Ellipsoid with
 *  Linear Constraints.
 *
 * @author Lakshmi Krishnamurthy
 */

public class ConstrainedCovarianceEllipsoid {

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

        double[][] aadblCovarianceMatrix = new double[][] {
            {0.09, 0.12},
            {0.12, 0.04}
        };

        double[] adblEqualityConstraint = new double[] {
            1.,
            1.
        };

        double dblEqualityConstraintConstant = -1.;

        AffineMultivariate lmConstraintRdToR1 = new AffineMultivariate (
            adblEqualityConstraint,
            dblEqualityConstraintConstant
        );

        CovarianceEllipsoidMultivariate ceObjectiveRdToR1 = new CovarianceEllipsoidMultivariate (aadblCovarianceMatrix);

        LagrangianMultivariate ceec = new LagrangianMultivariate (
            ceObjectiveRdToR1,
            new RdToR1[] {
                lmConstraintRdToR1
            }
        );

        double[][] aadblVariate = {
            {0.0, 1.0, 1.0},
            {0.1, 0.9, 1.0},
            {0.2, 0.8, 1.0},
            {0.3, 0.7, 1.0},
            {0.4, 0.6, 1.0},
            {0.5, 0.5, 1.0},
            {0.6, 0.4, 1.0},
            {0.7, 0.3, 1.0},
            {0.8, 0.2, 1.0},
            {0.9, 0.1, 1.0},
            {1.0, 0.0, 1.0},
        };

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

        System.out.println ("\t|       POINT VALUE      ||");

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

        for (double[] adblVariate : aadblVariate)
            System.out.println (
                "\t|  [" + adblVariate[0] +
                " | " + adblVariate[1] +
                "] = " + FormatUtil.FormatDouble (ceec.evaluate (adblVariate), 1, 4, 1.) + " ||"
            );

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

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

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

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

        for (double[] adblVariate : aadblVariate) {
            String strJacobian = "";

            double[] adblJacobian = ceec.jacobian (adblVariate);

            for (double dblJacobian : adblJacobian)
                strJacobian += FormatUtil.FormatDouble (dblJacobian, 1, 4, 1.) + ",";

            System.out.println (
                "\t|  [" + adblVariate[0] +
                " | " + adblVariate[1] +
                "] = {" + strJacobian + "} ||"
            );
        }

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

        double[][] aadblHessian = ceec.hessian (
            new double[] {
                0.20,
                0.80,
                1.
            }
        );

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

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

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

        for (double[] adblHessian : aadblHessian) {
            String strHessian = "";

            for (double dblHessian : adblHessian)
                strHessian += FormatUtil.FormatDouble (dblHessian, 1, 4, 1.) + ",";

            System.out.println ("\t| [" + strHessian + "] ||");
        }

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