BasisMonicBSpline.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 Samples for the Construction and the usage of various monic basis B Splines.
 *  It demonstrates the following:
 *  - Construction of segment B Spline 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 BasisMonicBSpline {

    /*
     * This sample illustrates the construction and the usage of the monic basis B Splines. It shows the
     *  following:
     *  - Construct the segment basis monic function from the specified hat type, the shape controller, the
     *      derivative order, and the tension.
     *  - Compare the responses emitted by the basis hat functions and the monic basis functions.
     *  - Compute the normalized cumulative emitted by the monic basis functions.
     *  - Compute the ordered derivative emitted by the monic basis functions.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void TestMonicHatBasis (
        final String strHatType,
        final String strShapeController,
        final TensionBasisHat[] aTBH,
        final double[] adblPredictorOrdinate,
        final String strTest)
        throws Exception
    {
        /*
         * Construct the segment basis monic function from the specified hat type, the shape controller, the
         *  derivative order, and the tension.
         */

        SegmentBasisFunction me = SegmentBasisFunctionGenerator.Monic (
            strHatType,
            strShapeController,
            adblPredictorOrdinate,
            2,
            aTBH[0].tension()
        );

        /*
         * Compare the responses emitted by the basis hat functions and the monic basis functions.
         */

        double dblX = 1.0;
        double dblXIncrement = 0.25;

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

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

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

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

        while (dblX <= 3.0) {
            System.out.println (
                "\tResponse[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (aTBH[0].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (aTBH[1].evaluate (dblX), 1, 5, 1.) + " | " +
                FormatUtil.FormatDouble (me.evaluate (dblX), 1, 5, 1.));

            dblX += dblXIncrement;
        }

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

        /*
         * Compute the normalized cumulative emitted by the monic basis functions.
         */

        dblX = 1.0;

        while (dblX <= 3.0) {
            System.out.println (
                "\t\tNormCumulative[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (me.normalizedCumulative (dblX), 1, 5, 1.)
            );

            dblX += dblXIncrement;
        }

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

        /*
         * Compute the ordered derivative emitted by the monic basis functions.
         */

        dblX = 1.0;
        int iOrder = 1;

        while (dblX <= 3.0) {
            System.out.println (
                "\t\t\tDeriv[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
                FormatUtil.FormatDouble (me.derivative (dblX, iOrder), 1, 5, 1.)
            );

            dblX += dblXIncrement;
        }

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

    /*
     * This sample illustrates the construction and usage of raw/processed basis tension splines, and their
     *  comparisons with the correspondingly constructed monic hat basis functions. It shows the following:
     *  - Construct the Processed Hyperbolic Tension Hat Pair from the co-ordinate arrays, the Ck, and the
     *      tension.
     *  - Implement and test the basis monic spline function using the constructed Processed Hyperbolic
     *      Tension Hat Pair and the Rational Linear Shape Controller.
     *  - Construct the Raw Hyperbolic Tension Hat Pair from the co-ordinate arrays and the tension.
     *  - Implement and test the basis monic spline function using the constructed Raw Hyperbolic Tension Hat
     *      Pair and the Rational Linear Shape Controller.
     *  - Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Linear
     *      Rational Shape Controller, and no tension.
     *  - Implement and test the basis monic spline function using the constructed Flat Processed Cubic
     *      Tension Hat Pair and the Rational Linear Shape Controller.
     *  - Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Linear
     *      Rational Shape Controller, and non-zero tension.
     *  - Implement and test the basis monic spline function using the constructed Processed Cubic Rational
     *      Tension Hat Pair and the Rational Linear Shape Controller.
     *  - Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Quadratic
     *      Rational Shape Controller, and the tension.
     *  - Implement and test the basis monic spline function using the constructed Processed Cubic Rational
     *      Tension Hat Pair and the Quadratic Linear Shape Controller.
     *  - Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Exponential
     *      Rational Shape Controller, and the tension.
     *  - Implement and test the basis monic spline function using the constructed Processed Cubic Rational
     *      Tension Hat Pair and the Rational Exponential Shape Controller.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void BasisMonicBSplineSample()
        throws Exception
    {
        double[] adblPredictorOrdinate = new double[] {1., 2., 3.};

        /*
         * Construct the Processed Hyperbolic Tension Hat Pair from the co-ordinate arrays, the Ck, and the
         *  tension.
         */

        TensionBasisHat[] aTBHProcessed = BasisHatPairGenerator.ProcessedHyperbolicTensionHatPair (
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            2,
            1.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Processed Hyperbolic
         *  Tension Hat Pair and the Rational Linear Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.PROCESSED_TENSION_HYPERBOLIC,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            aTBHProcessed,
            adblPredictorOrdinate,
            " PROCESSED HYPERBOLIC "
        );

        /*
         * Construct the Raw Hyperbolic Tension Hat Pair from the co-ordinate arrays and the tension.
         */

        TensionBasisHat[] aTBHStraight = BasisHatPairGenerator.HyperbolicTensionHatPair (
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            1.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Raw Hyperbolic Tension
         *  Hat Pair and the Rational Linear Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.RAW_TENSION_HYPERBOLIC,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            aTBHStraight,
            adblPredictorOrdinate,
            " STRAIGHT  HYPERBOLIC "
        );

        /*
         * Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Linear
         *  Rational Shape Controller, and no tension.
         */

        TensionBasisHat[] aTBHCubicRationalPlain = BasisHatPairGenerator.ProcessedCubicRationalHatPair (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            2,
            0.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Flat Processed Cubic
         *  Tension Hat Pair and the Rational Linear Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            aTBHCubicRationalPlain,
            adblPredictorOrdinate,
            "     CUBIC     FLAT   "
        );

        /*
         * Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Linear
         *  Rational Shape Controller, and non-zero tension.
         */

        TensionBasisHat[] aTBHCubicRationalLinear = BasisHatPairGenerator.ProcessedCubicRationalHatPair (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            2,
            1.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Processed Cubic Rational
         *  Tension Hat Pair and the Rational Linear Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            aTBHCubicRationalLinear,
            adblPredictorOrdinate,
            " CUBIC LINEAR RATIONAL "
        );

        /*
         * Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Quadratic
         *  Rational Shape Controller, and the tension.
         */

        TensionBasisHat[] aTBHCubicRationalQuadratic = BasisHatPairGenerator.ProcessedCubicRationalHatPair (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_QUADRATIC,
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            2,
            1.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Processed Cubic Rational
         *  Tension Hat Pair and the Quadratic Linear Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_QUADRATIC,
            aTBHCubicRationalQuadratic,
            adblPredictorOrdinate,
            " CUBIC  QUAD  RATIONAL "
        );

        /*
         * Construct the Processed Cubic Rational Tension Hat Pair from the co-ordinate arrays, Exponential
         *  Rational Shape Controller, and the tension.
         */

        TensionBasisHat[] aTBHCubicRationalExponential = BasisHatPairGenerator.ProcessedCubicRationalHatPair (
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_EXPONENTIAL,
            adblPredictorOrdinate[0],
            adblPredictorOrdinate[1],
            adblPredictorOrdinate[2],
            2,
            1.
        );

        /*
         * Implement and test the basis monic spline function using the constructed Processed Cubic Rational
         *  Tension Hat Pair and the Rational Exponential Shape Controller.
         */

        TestMonicHatBasis (
            BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_EXPONENTIAL,
            aTBHCubicRationalExponential,
            adblPredictorOrdinate,
            " CUBIC  EXP  RATIONAL "
        );
    }

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