KnotInsertionSequenceAdjuster.java

package org.drip.sample.stretch;

import org.drip.function.r1tor1.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.params.*;
import org.drip.spline.stretch.*;

/*
 * -*- 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.
 */

/**
 * KnotInsertionSequenceAdjuster demonstrates the Stretch Manipulation and Adjustment API. It shows the
 *  following:
 *  - Construct a simple Base Stretch.
 *  - Clip a left Portion of the Stretch to construct a left-clipped Stretch.
 *  - Clip a right Portion of the Stretch to construct a tight-clipped Stretch.
 *  - Compare the values across all the stretches to establish a) the continuity in the base smoothness is,
 *      preserved, and b) Continuity across the predictor ordinate for the implied response value is also
 *      preserved.
 *
 * @author Lakshmi Krishnamurthy
 */

public class KnotInsertionSequenceAdjuster {

    /*
     * Build Polynomial Segment Control Parameters
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final SegmentCustomBuilderControl PolynomialSegmentControlParams (
        final int iNumBasis,
        final SegmentInelasticDesignControl sdic,
        final ResponseScalingShapeControl rssc)
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
            new PolynomialFunctionSetParams (iNumBasis),
            sdic,
            rssc,
            null
        );
    }

    /*
     * Basis Spline Stretch Test Sample. Performs the following:
     *  - Construct the Array of Segment Builder Parameters - one per segment.
     *  - Construct the Stretch instance.
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final MultiSegmentSequence BasisSplineStretchTest (
        final double[] adblX,
        final double[] adblY,
        final SegmentCustomBuilderControl scbc)
        throws Exception
    {
        /*
         * Array of Segment Builder Parameters - one per segment
         */

        SegmentCustomBuilderControl[] aSCBC = new SegmentCustomBuilderControl[adblX.length - 1]; 

        for (int i = 0; i < adblX.length - 1; ++i)
            aSCBC[i] = scbc;

        /*
         * Construct a Stretch instance 
         */

        return MultiSegmentSequenceBuilder.CreateCalibratedStretchEstimator (
            "SPLINE_STRETCH",
            adblX, // predictors
            adblY, // responses
            aSCBC, // Basis Segment Builder parameters
            null,
            BoundarySettings.NaturalStandard(), // Boundary Condition - Natural
            MultiSegmentSequence.CALIBRATE // Calibrate the Stretch predictors to the responses
        );
    }

    /*
     * The Stretch Adjuster Test - this brings it altogether.
     */

    private static final void StretchAdjusterTest()
        throws Exception
    {
        /*
         * X predictors
         */

        double[] adblX = new double[] { 1.00,  1.50,  2.00, 3.00, 4.00, 5.00, 6.50, 8.00, 10.00};

        /*
         * Y responses
         */

        double[] adblY = new double[] {25.00, 20.25, 16.00, 9.00, 4.00, 1.00, 0.25, 4.00, 16.00};

        /*
         * Construct a rational shape controller with the shape controller tension of 1.
         */

        double dblShapeControllerTension = 1.;

        ResponseScalingShapeControl rssc = new ResponseScalingShapeControl (
            false,
            new QuadraticRationalShapeControl (dblShapeControllerTension)
        );

        /*
         * Construct the segment inelastic parameter that is C2 (iK = 2 sets it to C2), with 2nd order
         *  roughness penalty derivative, and without constraint
         */

        int iK = 2;
        int iRoughnessPenaltyDerivativeOrder = 2;

        SegmentInelasticDesignControl sdic = SegmentInelasticDesignControl.Create (
            iK,
            iRoughnessPenaltyDerivativeOrder
        );

        /*
         * Build the polynomial basis spline segment control parameters, and set up the stretch
         */

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

        int iPolyNumBasis = 4;

        SegmentCustomBuilderControl scbc = PolynomialSegmentControlParams (
            iPolyNumBasis,
            sdic,
            rssc
        );

        MultiSegmentSequence mssBase = BasisSplineStretchTest (
            adblX,
            adblY,
            scbc
        );

        /*
         * Estimate, compute the segment-by-segment monotonicity and the Stretch Jacobian
         */

        double dblX = mssBase.getLeftPredictorOrdinateEdge();

        double dblXMax = mssBase.getRightPredictorOrdinateEdge();

        while (dblX <= dblXMax) {
            System.out.println ("Y[" + dblX + "] " + FormatUtil.FormatDouble (mssBase.responseValue (dblX), 1, 2, 1.) + " | "
                + mssBase.monotoneType (dblX));

            System.out.println ("Jacobian Y[" + dblX + "]=" + mssBase.jackDResponseDCalibrationInput (dblX, 1).displayString());

            dblX += 1.;
        }

        /*
         * Clip part of the stretch left of the specified predictor ordinate
         */

        System.out.println ("\tSPLINE_STRETCH_BASE DPE: " + mssBase.curvatureDPE());

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

        MultiSegmentSequence mssLeftClipped = mssBase.clipLeft (
            "LEFT_CLIP",
            1.66
        );

        dblX = mssBase.getLeftPredictorOrdinateEdge();

        /*
         * Estimate, compute the segment-by-segment monotonicity and the Stretch Jacobian of the left clipped stretch
         */

        while (dblX <= dblXMax) {
            if (mssLeftClipped.in (dblX)) {
                System.out.println ("Y[" + dblX + "] " + FormatUtil.FormatDouble (mssLeftClipped.responseValue (dblX), 1, 2, 1.) + " | "
                    + mssLeftClipped.monotoneType (dblX));

                System.out.println ("Jacobian Y[" + dblX + "]=" + mssLeftClipped.jackDResponseDCalibrationInput (dblX, 1).displayString());
            }

            dblX += 1.;
        }

        /*
         * Left clipped stretch DPE
         */

        System.out.println ("\tSPLINE_STRETCH_LEFT DPE: " + mssLeftClipped.curvatureDPE());

        /*
         * Clip part of the stretch right of the specified predictor ordinate
         */

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

        MultiSegmentSequence mssRightClipped = mssBase.clipRight (
            "RIGHT_CLIP",
            7.48
        );

        /*
         * Estimate, compute the segment-by-segment monotonicity and the Stretch Jacobian of the right clipped stretch
         */

        dblX = mssBase.getLeftPredictorOrdinateEdge();

        while (dblX <= dblXMax) {
            if (mssRightClipped.in (dblX)) {
                System.out.println ("Y[" + dblX + "] " + FormatUtil.FormatDouble (mssRightClipped.responseValue (dblX), 1, 2, 1.) + " | "
                    + mssRightClipped.monotoneType (dblX));

                System.out.println ("Jacobian Y[" + dblX + "]=" + mssRightClipped.jackDResponseDCalibrationInput (dblX, 1).displayString());
            }

            dblX += 1.;
        }

        /*
         * Right clipped stretch DPE
         */

        System.out.println ("\tSPLINE_STRETCH_RIGHT DPE: " + mssRightClipped.curvatureDPE());

        /*
         * Ordered Side by side Comparison of left clipped - unclipped - right clipped response values
         */

        dblX = mssBase.getLeftPredictorOrdinateEdge();

        dblXMax = mssBase.getRightPredictorOrdinateEdge();

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

        System.out.println ("                           BASE         ||      LEFT CLIPPED           ||      RIGHT CLIPPED");

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

        while (dblX <= dblXMax) {
            java.lang.String strLeftClippedValue = "         ";
            java.lang.String strRightClippedValue = "         ";
            java.lang.String strLeftClippedMonotonocity = "             ";
            java.lang.String strRightClippedMonotonocity = "             ";

            /*
             * Unclipped
             */

            java.lang.String strDisplay = "Y[" + FormatUtil.FormatDouble (dblX, 2, 3, 1.) + "] => "
                + FormatUtil.FormatDouble (mssBase.responseValue (dblX), 2, 6, 1.) + " | "
                + mssBase.monotoneType (dblX);

            /*
             * Left clipped
             */

            if (mssLeftClipped.in (dblX)) {
                strLeftClippedValue = FormatUtil.FormatDouble (mssLeftClipped.responseValue (dblX), 2, 6, 1.);

                strLeftClippedMonotonocity = mssLeftClipped.monotoneType (dblX).toString();
            }

            /*
             * Right clipped
             */

            if (mssRightClipped.in (dblX)) {
                strRightClippedValue = FormatUtil.FormatDouble (mssRightClipped.responseValue (dblX), 2, 6, 1.);

                strRightClippedMonotonocity = mssRightClipped.monotoneType (dblX).toString();
            }

            System.out.println (strDisplay + "  ||  " + strLeftClippedValue + " | " + strLeftClippedMonotonocity +
                "  ||  " + strRightClippedValue + " | " + strRightClippedMonotonocity);

            dblX += 0.5;
        }
    }

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