BasisMonicHatComparison.java

package org.drip.sample.spline;

import org.drip.numerical.common.FormatUtil;
import org.drip.spline.bspline.*;

/*
 * -*- 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.
 */

/**
 * BasisMonicBSpline implements the comparison of the basis hat functions used in the construction of the
 *  monic basis B Splines. It demonstrates the following:
 *  - Construction of the Linear Cubic Rational Raw Hat Functions
 *  - Construction of the Quadratic Cubic Rational Raw Hat Functions
 *  - Construction of the Corresponding Processed Tension Basis Hat Functions
 *  - Construction of the Wrapping Monic Functions
 *  - Estimation and Comparison of the Ordered Derivatives
 *
 * @author Lakshmi Krishnamurthy
 */

public class BasisMonicHatComparison {

    /*
     * This sample display the test of the different shape controller functions. It demonstrates the
     *  following:
     *  - Construct the Raw Cubic rational left Tension Basis using the specified shape controller and
     *      tension.
     *  - Construct the Raw Cubic rational right Tension Basis using the specified shape controller and
     *      tension.
     *  - Construct the processed Cubic rational left Tension Basis using the Raw Cubic rational left Tension
     *      Basis.
     *  - Construct the processed Cubic rational Right Tension Basis using the Raw Cubic rational Right
     *      Tension Basis.
     *  - Construct the Segment Monic Basis Function using the left and the right processed hat functions.
     *  - Display the response and the derivatives for the left/right cubic rational, and their corresponding
     *      processed tension hat basis functions.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void ShapeControllerTest (
        final String strShapeController,
        final double dblTension)
        throws Exception
    {
        /*
         * Construct the Raw Cubic rational left Tension Basis using the specified shape controller and
         *  tension.
         */

        CubicRationalLeftRaw crlr = new CubicRationalLeftRaw (
            1.,
            2.,
            strShapeController,
            dblTension
        );

        /*
         * Construct the Raw Cubic rational right Tension Basis using the specified shape controller and
         *  tension.
         */

        CubicRationalRightRaw crrr = new CubicRationalRightRaw (
            2.,
            3.,
            strShapeController,
            dblTension
        );

        /*
         * Construct the processed Cubic rational left Tension Basis using the Raw Cubic rational left
         *  Tension Basis.
         */

        TensionProcessedBasisHat tpbhLeft = new TensionProcessedBasisHat (
            crlr,
            2
        );

        /*
         * Construct the processed Cubic rational right Tension Basis using the Raw Cubic rational Right
         *  Tension Basis.
         */

        TensionProcessedBasisHat tpbhRight = new TensionProcessedBasisHat (
            crrr,
            2
        );

        /*
         * Construct the Segment Monic Basis Function using the left and the right processed hat functions.
         */

        SegmentMonicBasisFunction smbf = new SegmentMonicBasisFunction (
            tpbhLeft,
            tpbhRight
        );

        /*
         * Display the response and the derivatives for the left/right cubic rational, and their
         *  corresponding processed tension hat basis functions.
         */

        double dblX = crlr.left();

        while (dblX <= crrr.right()) {
            System.out.println ("\tDeriv[" + dblX + "] => " +
                FormatUtil.FormatDouble (smbf.derivative (dblX, 1), 1, 5, 1.));

            System.out.println ("\t\tCubic Rational Left Deriv[" + dblX + "]  => " +
                FormatUtil.FormatDouble (crlr.derivative (dblX, 3), 1, 5, 1.));

            System.out.println ("\t\tCubic Rational Right Deriv[" + dblX + "] => " +
                FormatUtil.FormatDouble (crrr.derivative (dblX, 3), 1, 5, 1.));

            System.out.println ("\t\tTPBH Left Deriv[" + dblX + "]  => " +
                FormatUtil.FormatDouble (tpbhLeft.derivative (dblX, 1), 1, 5, 1.));

            System.out.println ("\t\tTPBH Right Deriv[" + dblX + "] => " +
                FormatUtil.FormatDouble (tpbhRight.derivative (dblX, 1), 1, 5, 1.));

            dblX += 0.5;
        }
    }

    /*
     * Sample illustrating the construction and usage of different monic basis hat shape controllers. This
     *  example illustrates the following:
     *  - Test Rational Linear Shape Control with 0.0 Tension Parameter (i.e., no shape control).
     *  - Test Rational Linear Shape Control with 1.0 Tension Parameter.
     *  - Test Rational Quadratic Shape Control with 1.0 Tension Parameter.
     *  - Test Exponential Shape Control with 1.0 Tension Parameter.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void BasisMonicHatComparisonSample()
        throws Exception
    {
        /*
         * Test Rational Linear Shape Control with 0.0 Tension Parameter (i.e., no shape control)
         */

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

        System.out.println ("----------------- NO SHAPE CONTROL --------------------------------");

        System.out.println ("-------------------------------------------------------------------");

        ShapeControllerTest (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            0.
        );

        /*
         * Test Rational Linear Shape Control with 1.0 Tension Parameter
         */

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

        System.out.println ("----------------- LINEAR SHAPE CONTROL; Tension 1.0 ---------------");

        System.out.println ("-------------------------------------------------------------------");

        ShapeControllerTest (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            1.
        );

        /*
         * Test Rational Quadratic Shape Control with 1.0 Tension Parameter
         */

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

        System.out.println ("-------------- QUADRATIC SHAPE CONTROL; Tension 1.0 ---------------");

        System.out.println ("-------------------------------------------------------------------");

        ShapeControllerTest (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_QUADRATIC,
            1.
        );

        /*
         * Test Exponential Shape Control with 1.0 Tension Parameter
         */

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

        System.out.println ("-------------- EXPONENTIAL SHAPE CONTROL; Tension 1.0 ---------------");

        System.out.println ("-------------------------------------------------------------------");

        ShapeControllerTest (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_EXPONENTIAL,
            1.
        );
    }

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