IntegrandQuadrature.java

package org.drip.sample.numerical;

import org.drip.function.definition.R1ToR1;
import org.drip.function.r1tor1.*;
import org.drip.numerical.common.*;
import org.drip.numerical.integration.R1ToR1Integrator;

/*
 * -*- 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
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * Copyright (C) 2014 Lakshmi Krishnamurthy
 * Copyright (C) 2013 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.
 */

/**
 * IntegrandQuadrature shows samples for the following routines for integrating the objective function:
 *  - Mid-Point Scheme
 *  - Trapezoidal Scheme
 *  - Simpson/Simpson38 schemes
 *  - Boole Scheme
 * 
 * @author Lakshmi Krishnamurthy
 */

public class IntegrandQuadrature {

    /*
     * Compute the Integrand Quadrature for the specified Univariate Function using the various methods.
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static void ComputeQuadrature (
        final R1ToR1 au,
        final double dblActual,
        final double dblStart,
        final double dblEnd)
        throws Exception
    {
        int iRightDecimal = 8;

        System.out.println ("\t\tActual      : " +
            FormatUtil.FormatDouble (dblActual, 1, iRightDecimal, 1.)
        );

        System.out.println ("\t\tLinear      : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.LinearQuadrature (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );

        System.out.println ("\t\tMidPoint     : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.MidPoint (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );

        System.out.println ("\t\tTrapezoidal  : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.Trapezoidal (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );

        System.out.println ("\t\tSimpson      : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.Simpson (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );

        System.out.println ("\t\tSimpson 38   : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.Simpson38 (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );

        System.out.println ("\t\tBoole        : " +
            FormatUtil.FormatDouble (
                R1ToR1Integrator.Boole (
                    au,
                    dblStart,
                    dblEnd
                ),
                1,
                iRightDecimal,
                1.
            )
        );
    }

    /*
     * Compute the Integrand Quadrature for the various Univariate Functions using the different methods.
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static void IntegrandQuadratureSample()
        throws Exception
    {
        double dblStart = 0.;
        double dblEnd = 1.;

        R1ToR1 auExp = new ExponentialTension (
            Math.E,
            1.
        );

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

        ComputeQuadrature (
            auExp,
            auExp.evaluate (dblEnd) - auExp.evaluate (dblStart),
            dblStart,
            dblEnd
        );

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

        R1ToR1 au1 = new R1ToR1 (null) {
            @Override public double evaluate (
                final double dblVariate)
                throws Exception
            {
                return Math.cos (dblVariate) - dblVariate * dblVariate * dblVariate;
            }
        };

        ComputeQuadrature (
            au1,
            Math.sin (dblEnd) - Math.sin (dblStart) - 0.25 * (dblEnd * dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart * dblStart),
            dblStart,
            dblEnd
        );

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

        R1ToR1 au2 = new R1ToR1 (null) {
            @Override public double evaluate (
                final double dblVariate)
                throws Exception
            {
                return dblVariate * dblVariate * dblVariate - 3. * dblVariate * dblVariate + 2. * dblVariate;
            }
        };

        ComputeQuadrature (
            au2,
            0.25 * (dblEnd * dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart * dblStart) -
                (dblEnd * dblEnd * dblEnd - dblStart * dblStart * dblStart) +
                (dblEnd * dblEnd - dblStart * dblStart),
            dblStart,
            dblEnd
        );

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

    public static void main (
        final String astrArgs[])
        throws Exception
    {
        IntegrandQuadratureSample();
    }
}