KnotInsertionTensionEstimator.java

    
package org.drip.sample.stretch;

import org.drip.function.r1tor1.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.spline.basis.*;
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.
 */

/**
 * KnotInsertionTensionEstimator demonstrates the Stretch builder and usage API. It shows the following:
 * 
 *  - Construction of segment control parameters - polynomial (regular/Bernstein) segment control,
 *      exponential/hyperbolic tension segment control, Kaklis-Pandelis tension segment control.
 *  - Tension Basis Spline Test using the specified predictor/response set and the array of segment custom
 *      builder control parameters.
 *  - Complete the full tension stretch estimation sample test.
 *
 * @author Lakshmi Krishnamurthy
 */

public class KnotInsertionTensionEstimator {

    /*
     * Build KLK Exponential Tension Segment Control Parameters
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final SegmentCustomBuilderControl KLKExponentialTensionSegmentControlParams (
        final double dblTension,
        final SegmentInelasticDesignControl sdic,
        final ResponseScalingShapeControl rssc)
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_KLK_EXPONENTIAL_TENSION,
            new ExponentialTensionSetParams (dblTension),
            sdic,
            rssc,
            null
        );
    }

    /*
     * Build KLK Hyperbolic Tension Segment Control Parameters
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final SegmentCustomBuilderControl KLKHyperbolicTensionSegmentControlParams (
        final double dblTension,
        final SegmentInelasticDesignControl sdic,
        final ResponseScalingShapeControl rssc)
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_KLK_HYPERBOLIC_TENSION,
            new ExponentialTensionSetParams (dblTension),
            sdic,
            rssc,
            null
        );
    }

    /*
     * Build KLK Rational Linear Tension Segment Control Parameters
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final SegmentCustomBuilderControl KLKRationalLinearTensionSegmentControlParams (
        final double dblTension,
        final SegmentInelasticDesignControl sdic,
        final ResponseScalingShapeControl rssc)
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_KLK_RATIONAL_LINEAR_TENSION,
            new ExponentialTensionSetParams (dblTension),
            sdic,
            rssc,
            null
        );
    }

    /*
     * Build KLK Rational Quadratic Tension Segment Control Parameters
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final SegmentCustomBuilderControl KLKRationalQuadraticTensionSegmentControlParams (
        final double dblTension,
        final SegmentInelasticDesignControl sdic,
        final ResponseScalingShapeControl rssc)
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_KLK_RATIONAL_QUADRATIC_TENSION,
            new ExponentialTensionSetParams (dblTension),
            sdic,
            rssc,
            null
        );
    }

    /*
     * Tension Basis Spline Test using the specified predictor/response set and the array of segment custom
     *  builder control parameters. It consists of the following steps:
     *  - Array of Segment Builder Parameters - one per segment
     *  - Construct a Stretch instance
     *  - Estimate, compute the segment-by-segment monotonicity and the Stretch Jacobian
     *  - Construct a new Stretch instance by inserting a pair of of predictor/response knots
     *  - Estimate, compute the segment-by-segment monotonicity and the Stretch Jacobian
     * 
     *  WARNING: Insufficient Error Checking, so use caution
     */

    private static final void BasisSplineStretchTest (
        final double[] adblX,
        final double[] adblY,
        final SegmentCustomBuilderControl scbc)
        throws Exception
    {
        double dblX = 1.;
        double dblXMax = 10.;

        /*
         * 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 
         */

        MultiSegmentSequence mss = 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
        );

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

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

            System.out.println ("\tJacobian Y[" + dblX + "]=" + mss.jackDResponseDCalibrationInput (dblX, 1).displayString());

            dblX += 1.;
        }

        System.out.println ("\t\tSPLINE_STRETCH DPE: " + mss.curvatureDPE());

        /*
         * Construct a new Stretch instance by inserting a pair of of predictor/response knots
         */

        MultiSegmentSequence mssInsert = MultiSegmentSequenceModifier.InsertKnot (mss,
            9.,
            10.,
            BoundarySettings.NaturalStandard(), // Boundary Condition - Natural
            MultiSegmentSequence.CALIBRATE // Calibrate the Stretch predictors to the responses
        );

        dblX = 1.;

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

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

            dblX += 1.;
        }

        System.out.println ("\t\tSPLINE_STRETCH_INSERT DPE: " + mssInsert.curvatureDPE());
    }

    /*
     * Complete the full tension stretch estimation sample test by doing the following:
     *  - Composing the array of predictor/responses
     *  - Construct a rational shape controller with the desired shape controller tension
     *  - Construct the Segment Inelastic Parameter that is C2 (iK = 2 sets it to C2), with Second Order
     *      Curvature Penalty Derivative, and without constraint
     *  - KLK Hyperbolic Tension Basis Spline Stretch Test
     *  - KLK Exponential Tension Basis Spline Stretch Test
     *  - KLK Rational Linear Tension Basis Spline Stretch Test
     *  - KLK Rational Quadratic Tension Basis Spline Stretch Test
     */

    public static final void TensionStretchEstimationSample()
        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 LinearRationalShapeControl (dblShapeControllerTension)
        );

        /*
         * Construct the Segment Inelastic Parameter that is C2 (iK = 2 sets it to C2), with Second Order
         *  Curvature Penalty Derivative, and without constraint
         */

        int iK = 2;
        int iCurvaturePenaltyDerivativeOrder= 2;

        SegmentInelasticDesignControl segParams = SegmentInelasticDesignControl.Create (
            iK,
            iCurvaturePenaltyDerivativeOrder
        );

        double dblKLKTension = 1.;

        /*
         * KLK Hyperbolic Tension Basis Spline Stretch Test
         */

        System.out.println (" \n---------- \n KLK HYPERBOLIC TENSION \n ---------- \n");

        BasisSplineStretchTest (
            adblX,
            adblY,
            KLKHyperbolicTensionSegmentControlParams (
                dblKLKTension,
                segParams,
                rssc
            )
        );

        /*
         * KLK Exponential Tension Basis Spline Stretch Test
         */

        System.out.println (" \n---------- \n KLK EXPONENTIAL TENSION \n ---------- \n");

        BasisSplineStretchTest (
            adblX,
            adblY,
            KLKExponentialTensionSegmentControlParams (
                dblKLKTension,
                segParams,
                rssc
            )
        );

        /*
         * KLK Rational Linear Tension Basis Spline Stretch Test
         */

        System.out.println (" \n---------- \n KLK RATIONAL LINEAR TENSION \n ---------- \n");

        BasisSplineStretchTest (
            adblX,
            adblY,
            KLKRationalLinearTensionSegmentControlParams (
                dblKLKTension,
                segParams,
                rssc
            )
        );

        /*
         * KLK Rational Quadratic Tension Basis Spline Stretch Test
         */

        System.out.println (" \n---------- \n KLK RATIONAL QUADRATIC TENSION \n ---------- \n");

        BasisSplineStretchTest (
            adblX,
            adblY,
            KLKRationalQuadraticTensionSegmentControlParams (
                dblKLKTension,
                segParams,
                rssc
            )
        );
    }

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