BSplineSequence.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.
 */

/**
 * BSplineSequence implements Samples for the Construction and the usage of various monic basis B Spline
 *  Sequences. It demonstrates the following:
 *  - Construction and Usage of segment Monic B Spline Sequence.
 *  - Construction and Usage of segment Multic B Spline Sequence.
 *
 * @author Lakshmi Krishnamurthy
 */

public class BSplineSequence {

    /*
     * This sample shows the computation of the response value, the normalized cumulative, and the ordered
     *  derivative of the specified Segment Basis Function.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void ComputeResponseMetric (
        final SegmentBasisFunction me,
        final String strComment)
        throws Exception
    {
        int iOrder = 1;
        double dblXIncrement = 0.25;

        double dblX = me.leading() - dblXIncrement;

        double dblXEnd = me.trailing() + dblXIncrement;

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

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

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

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

            dblX += dblXIncrement;
        }
    }

    /*
     * This sample demonstrates the construction and usage of the following monic/multic basis spline arrays:
     *  - Hyperbolic Rational Linear Monic.
     *  - Multic basis functions of 3rd degree (i.e., quadratic).
     *  - Multic basis functions of 4th degree (i.e., cubic).
     *  - Multic basis functions of 5th degree (i.e., quartic).
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final void BSplineSequenceSample()
        throws Exception
    {
        double[] adblPredictorOrdinate = new double[] {
            1., 2., 3., 4., 5., 6.
        };

        /*
         * Construct the Array of Hyperbolic Rational Linear Monic Segment Basis Functions. 
         */

        SegmentBasisFunction[] aMonic = SegmentBasisFunctionGenerator.MonicSequence (
            BasisHatPairGenerator.RAW_TENSION_HYPERBOLIC,
            BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
            adblPredictorOrdinate,
            0,
            1.
        );

        /*
         * Display the response value, the normalized cumulative, and the ordered derivative of the Monic
         *  Segment Basis Function.
         */

        for (int i = 0; i < aMonic.length; ++i)
            ComputeResponseMetric (
                aMonic[i],
                "   MONIC   "
            );

        /*
         * Construct the array of multic basis functions of 3rd degree (i.e., quadratic).
         */

        SegmentBasisFunction[] aQuadratic = SegmentBasisFunctionGenerator.MulticSequence (
            3,
            aMonic
        );

        /*
         * Display the response value, the normalized cumulative, and the ordered derivative of the Quadratic
         *  Multic Segment Basis Function.
         */

        for (int i = 0; i < aQuadratic.length; ++i)
            ComputeResponseMetric (
                aQuadratic[i],
                " QUADRATIC "
            );

        /*
         * Construct the array of multic basis functions of 4th degree (i.e., cubic).
         */

        SegmentBasisFunction[] aCubic = SegmentBasisFunctionGenerator.MulticSequence (
            4,
            aQuadratic
        );

        /*
         * Display the response value, the normalized cumulative, and the ordered derivative of the Cubic
         *  Multic Segment Basis Function.
         */

        for (int i = 0; i < aCubic.length; ++i)
            ComputeResponseMetric (
                aCubic[i],
                "   CUBIC   "
            );

        /*
         * Construct the array of multic basis functions of 5th degree (i.e., quartic).
         */

        SegmentBasisFunction[] aQuartic = SegmentBasisFunctionGenerator.MulticSequence (
            5,
            aCubic
        );

        /*
         * Display the response value, the normalized cumulative, and the ordered derivative of the Quartic
         *  Multic Segment Basis Function.
         */

        for (int i = 0; i < aQuartic.length; ++i)
            ComputeResponseMetric (
                aQuartic[i],
                "  QUARTIC  "
            );
    }

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