BasisMulticBSpline.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.
 */

/**
 * BasisMulticBSpline implements Samples for the Construction and the usage of various multic basis B Splines.
 *  It demonstrates the following:
 *  - Construction of segment higher order B Spline from the corresponding Hat Basis Functions.
 *  - Estimation of the derivatives and the basis envelope cumulative integrands.
 *  - Estimation of the normalizer and the basis envelope cumulative normalized integrands.
 *
 * @author Lakshmi Krishnamurthy
 */

public class BasisMulticBSpline {

    /*
     * This sample illustrates the construction and the usage of multic basis functions, and their eventual
     *  response/derivative computation and comparison with the corresponding raw/processed and monic basis.
     *  It shows the following:
     *  - Construct the hyperbolic tension basis hat pair using the left predictor ordinates and the tension.
     *  - Construct the hyperbolic tension basis hat pair using the right predictor ordinates and the
     *      tension.
     *  - Generate the left monic basis function from the hat type, left predictor ordinates, shape control,
     *      and the tension parameters.
     *  - Generate the right monic basis function from the hat type, right predictor ordinates, shape
     *      control, and the tension parameters.
     *  - Run a response value calculation comparison across the predictor ordinates for each of the left
     *      basis hat and the monic basis functions.
     *  - Run a response value calculation comparison across the predictor ordinates for each of the right
     *      basis hat and the monic basis functions.
     *  - Construct a multic basis function using the left/right monic basis functions, and the multic order.
     *  - Display the multic Basis Function response as well as normalized Cumulative across the specified
     *      variate range.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void RunMulticBSplineTest (
        final String strHatType,
        final String strShapeControlType,
        final double dblTension,
        final int iMulticBSplineOrder)
        throws Exception
    {
        double[] adblPredictorOrdinateLeft = new double[] {
            1., 2., 3.
        };
        double[] adblPredictorOrdinateRight = new double[] {
            2., 3., 4.
        };

        /*
         * Construct the hyperbolic tension basis hat pair using the left predictor ordinates and the
         *  tension.
         */

        TensionBasisHat[] aTBHLeft = BasisHatPairGenerator.HyperbolicTensionHatPair (
            adblPredictorOrdinateLeft[0],
            adblPredictorOrdinateLeft[1],
            adblPredictorOrdinateLeft[2],
            dblTension
        );

        /*
         * Construct the hyperbolic tension basis hat pair using the right predictor ordinates and the
         *  tension.
         */

        TensionBasisHat[] aTBHRight = BasisHatPairGenerator.HyperbolicTensionHatPair (
            adblPredictorOrdinateRight[0],
            adblPredictorOrdinateRight[1],
            adblPredictorOrdinateRight[2],
            dblTension
        );

        /*
         * Generate the left monic basis function from the hat type, left predictor ordinates, shape control,
         *  and the tension parameters.
         */

        SegmentBasisFunction sbfMonicLeft = SegmentBasisFunctionGenerator.Monic (
            strHatType,
            strShapeControlType,
            adblPredictorOrdinateLeft,
            2,
            dblTension
        );

        /*
         * Generate the right monic basis function from the hat type, right predictor ordinates, shape
         *  control, and the tension parameters.
         */

        SegmentBasisFunction sbfMonicRight = SegmentBasisFunctionGenerator.Monic (
            strHatType,
            strShapeControlType,
            adblPredictorOrdinateRight,
            2,
            dblTension
        );

        /*
         * Run a response value calculation comparison across the predictor ordinates for each of the left
         *  basis hat and the monic basis functions.
         */

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

        System.out.println ("\t            X    |   LEFT   |   RIGHT  |   MONIC  ");

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

        double dblX = 0.50;
        double dblXIncrement = 0.25;

        while (dblX <= 4.50) {
            System.out.println (
                "\tResponse[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (aTBHLeft[0].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (aTBHLeft[1].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (sbfMonicLeft.evaluate (dblX), 1, 5, 1.)
            );

            dblX += dblXIncrement;
        }

        /*
         * Run a response value calculation comparison across the predictor ordinates for each of the right
         *  basis hat and the monic basis functions.
         */

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

        System.out.println ("\t            X    |   LEFT   |   RIGHT  |   MONIC  ");

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

        dblX = 0.50;

        while (dblX <= 4.50) {
            System.out.println (
                "\tResponse[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (aTBHRight[0].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (aTBHRight[1].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (sbfMonicRight.evaluate (dblX), 1, 5, 1.)
            );

            dblX += dblXIncrement;
        }

        /*
         * Construct a multic basis function using the left/right monic basis functions, and the multic
         *  order.
         */

        SegmentBasisFunction[] sbfMultic = SegmentBasisFunctionGenerator.MulticSequence (
            iMulticBSplineOrder,
            new SegmentBasisFunction[] {
                sbfMonicLeft,
                sbfMonicRight
            }
        );

        /*
         * Display the multic Basis Function response as well as normalized Cumulative across the specified
         *  variate range.
         */

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

        System.out.println ("\t          PREDICTOR    | RESPONSE | CUMULATIVE  ");

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

        dblX = 0.50;
        dblXIncrement = 0.125;

        while (dblX <= 4.50) {
            System.out.println (
                "\t\tMultic[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (sbfMultic[0].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (sbfMultic[0].normalizedCumulative (dblX), 1, 5, 1.)
            );

            dblX += dblXIncrement;
        }

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

    /*
     * This sample illustrates a sequence of tests using basis multic B Splines. In particular it shows the
     *  following:
     *  - Creation and usage of Multic B Spline built off of raw hyperbolic tension basis function, rational
     *      linear shape controller, tension = 1.0, and 3rd order multic.
     *  - Creation and usage of Multic B Spline built off of processed hyperbolic tension basis function,
     *      rational linear shape controller, tension = 1.0, and 3rd order multic.
     *  - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
     *      linear shape controller, tension = 0.0, and 3rd order multic.
     *  - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
     *      linear shape controller, tension = 1.0, and 3rd order multic.
     *  - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
     *      quadratic shape controller, tension = 1.0, and 3rd order multic.
     *  - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
     *      exponential shape controller, tension = 1.0, and 3rd order multic.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void BasisMulticBSplineSample()
        throws Exception
    {
        /*
         * Creation and usage of Multic B Spline built off of raw hyperbolic tension basis function,
         *  rational linear shape controller, tension = 1.0, and 3rd order multic.
         */

        System.out.println ("\n    RAW TENSION HYPERBOLIC | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.RAW_TENSION_HYPERBOLIC,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            1.,
            3
        );

        /*
         * Creation and usage of Multic B Spline built off of processed hyperbolic tension basis function,
         *  rational linear shape controller, tension = 1.0, and 3rd order multic.
         */

        System.out.println ("\n   PROC TENSION HYPERBOLIC | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.PROCESSED_TENSION_HYPERBOLIC,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            1.,
            3
        );

        /*
         * Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
         *  linear shape controller, tension = 0.0, and 3rd order multic.
         */

        System.out.println ("\n   RAW CUBIC RATIONAL | LINEAR SHAPE CONTROL | TENSION = 0.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            0.,
            3
        );

        /*
         * Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
         *  linear shape controller, tension = 1.0, and 3rd order multic.
         */

        System.out.println ("\n   RAW CUBIC RATIONAL | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            1.,
            3
        );

        /*
         * Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
         *  quadratic shape controller, tension = 1.0, and 3rd order multic.
         */

        System.out.println ("\n   RAW CUBIC RATIONAL | QUADRATIC SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_QUADRATIC,
            1.,
            3
        );

        /*
         * Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
         *  exponential shape controller, tension = 1.0, and 3rd order multic.
         */

        System.out.println ("\n   RAW CUBIC RATIONAL | EXPONENTIAL SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");

        RunMulticBSplineTest (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_EXPONENTIAL,
            1.,
            3
        );
    }

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