CurvatureLengthRoughnessPenalty.java

  1. package org.drip.sample.stretch;

  3. import org.drip.function.r1tor1.QuadraticRationalShapeControl;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.spline.basis.PolynomialFunctionSetParams;
  6. import org.drip.spline.params.*;
  7. import org.drip.spline.stretch.*;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */

  13. /*!
  14.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  17.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  19.  * Copyright (C) 2013 Lakshmi Krishnamurthy
  20.  * 
  21.  *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
  22.  *      libraries targeting analysts and developers
  23.  *      https://lakshmidrip.github.io/DRIP/
  24.  *  
  25.  *  DRIP is composed of four main libraries:
  26.  *  
  27.  *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
  28.  *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
  29.  *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
  30.  *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
  31.  * 
  32.  *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
  33.  *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
  34.  *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
  35.  *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
  36.  *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
  37.  * 
  38.  *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
  39.  *      Incorporator, Holdings Constraint, and Transaction Costs.
  40.  * 
  41.  *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
  42.  * 
  43.  *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
  44.  * 
  45.  *  Licensed under the Apache License, Version 2.0 (the "License");
  46.  *      you may not use this file except in compliance with the License.
  47.  *   
  48.  *  You may obtain a copy of the License at
  49.  *      http://www.apache.org/licenses/LICENSE-2.0
  50.  *  
  51.  *  Unless required by applicable law or agreed to in writing, software
  52.  *      distributed under the License is distributed on an "AS IS" BASIS,
  53.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  54.  *  
  55.  *  See the License for the specific language governing permissions and
  56.  *      limitations under the License.
  57.  */

  59. /**
  60.  * PenalizedCurvatureLCurvatureLengthRoughnessPenaltyengthFit demonstrates the setting up and the usage of
  61.  *  the curvature, the length, and the closeness of fit penalizing spline. This sample shows the following:
  62.  *  - Set up the X Predictor Ordinate and the Y Response Value Set.
  63.  *  - Construct a set of Predictor Ordinates, their Responses, and corresponding Weights to serve as
  64.  *      weighted closeness of fit.
  65.  *  - Construct a rational shape controller with the desired shape controller tension parameters and Global
  66.  *      Scaling.
  67.  *  - Construct the Segment Inelastic Parameter that is C2 (iK = 2 sets it to C2), with First Order Segment
  68.  *      Length Penalty Derivative, Second Order Segment Curvature Penalty Derivative, their Amplitudes, and
  69.  *      without Constraint.
  70.  *  - Construct the base, the base + 1 degree segment builder control.
  71.  *  - Construct the base, the elevated, and the best fit basis spline stretches.
  72.  *  - Compute the segment-by-segment monotonicity for all the three stretches.
  73.  *  - Compute the Stretch Jacobian for all the three stretches.
  74.  *  - Compute the Base Stretch Curvature, Length, and the Best Fit DPE.
  75.  *  - Compute the Elevated Stretch Curvature, Length, and the Best Fit DPE.
  76.  *  - Compute the Best Fit Stretch Curvature, Length, and the Best Fit DPE.
  77.  *
  78.  * @author Lakshmi Krishnamurthy
  79.  */

  81. public class CurvatureLengthRoughnessPenalty {

  83.     /*
  84.      * Build Polynomial Segment Control Parameters
  85.      * 
  86.      *  WARNING: Insufficient Error Checking, so use caution
  87.      */

  89.     public static final SegmentCustomBuilderControl PolynomialSegmentControlParams (
  90.         final int iNumBasis,
  91.         final SegmentInelasticDesignControl sdic,
  92.         final ResponseScalingShapeControl rssc)
  93.         throws Exception
  94.     {
  95.         return new SegmentCustomBuilderControl (
  96.             MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
  97.             new PolynomialFunctionSetParams (iNumBasis),
  98.             sdic,
  99.             rssc,
  100.             null
  101.         );
  102.     }

  104.     /*
  105.      * Construct the Basis Spline Stretch Instance using the following inputs:
  106.      *  - Array of Segment Builder Parameters - one per segment
  107.      *  - Construct a Calibrated Stretch instance
  108.      * 
  109.      *  WARNING: Insufficient Error Checking, so use caution
  110.      */

  112.     public static final MultiSegmentSequence BasisSplineStretchTest (
  113.         final double[] adblX,
  114.         final double[] adblY,
  115.         final SegmentCustomBuilderControl scbc,
  116.         final StretchBestFitResponse rbfr)
  117.         throws Exception
  118.     {
  119.         /*
  120.          * Array of Segment Builder Parameters - one per segment
  121.          */

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

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

  128.         /*
  129.          * Construct a Stretch instance 
  130.          */

  132.         return MultiSegmentSequenceBuilder.CreateCalibratedStretchEstimator (
  133.             "SPLINE_STRETCH",
  134.             adblX, // predictors
  135.             adblY, // responses
  136.             aSCBC, // Basis Segment Builder parameters
  137.             rbfr, // Fitness Weighted Response
  138.             BoundarySettings.NaturalStandard(), // Boundary Condition - Natural
  139.             MultiSegmentSequence.CALIBRATE // Calibrate the Stretch predictors to the responses
  140.         );
  141.     }

  143.     /*
  144.      * Illustrate the Penalized Curvature+Length+BestFit Usage Sample. This sample shows the following:
  145.      *  - Set up the X Predictor Ordinate and the Y Response Value Set.
  146.      *  - Construct a set of Predictor Ordinates, their Responses, and corresponding Weights to serve as
  147.      *      weighted closeness of fit.
  148.      *  - Construct a rational shape controller with the desired shape controller tension parameters and Global Scaling.
  149.      *  - Construct the Segment Inelastic Parameter that is C2 (iK = 2 sets it to C2), with First Order
  150.      *      Segment Length Penalty Derivative, Second Order Segment Curvature Penalty Derivative, their
  151.      *      Amplitudes, and without Constraint.
  152.      *  - Construct the base, the base + 1 degree segment builder control.
  153.      *  - Construct the base, the elevated, and the best fit basis spline stretches.
  154.      *  - Compute the segment-by-segment monotonicity for all the three stretches.
  155.      *  - Compute the Stretch Jacobian for all the three stretches.
  156.      *  - Compute the Base Stretch Curvature, Length, and the Best Fit DPE.
  157.      *  - Compute the Elevated Stretch Curvature, Length, and the Best Fit DPE.
  158.      *  - Compute the Best Fit Stretch Curvature, Length, and the Best Fit DPE.
  159.      */

  161.     public static final void PenalizedCurvatureLengthFitTest()
  162.         throws Exception
  163.     {
  164.         /*
  165.          * X predictors
  166.          */

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

  170.         /*
  171.          * Y responses
  172.          */

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

  176.         /*
  177.          * Construct a set of Predictor Ordinates, their Responses, and corresponding Weights to serve as
  178.          *  weighted closeness of fit.
  179.          */

  181.         StretchBestFitResponse rbfr = StretchBestFitResponse.Create (
  182.             new double[] { 2.28,  2.52,  2.73, 3.00,  5.50, 8.44,  8.76,  9.08,  9.80,  9.92},
  183.             new double[] {14.27, 12.36, 10.61, 9.25, -0.50, 7.92, 10.07, 12.23, 15.51, 16.36},
  184.             new double[] { 1.09,  0.82,  1.34, 1.10,  0.50, 0.79,  0.65,  0.49,  0.24,  0.21}
  185.         );

  187.         /*
  188.          * Construct a rational shape controller with the shape controller tension of 1, and Global Scaling.
  189.          */

  191.         double dblShapeControllerTension = 1.;

  193.         ResponseScalingShapeControl rssc = new ResponseScalingShapeControl (
  194.             false,
  195.             new QuadraticRationalShapeControl (dblShapeControllerTension)
  196.         );

  198.         /*
  199.          * Construct the Segment Inelastic Parameter that is C2 (iK = 2 sets it to C2), with First Order
  200.          *  Segment Length Penalty Derivative, Second Order Segment Curvature Penalty Derivative, their
  201.          *  Amplitudes, and without Constraint
  202.          */

  204.         int iK = 2;
  205.         double dblLengthPenaltyAmplitude = 1.;
  206.         double dblCurvaturePenaltyAmplitude = 1.;
  207.         int iLengthPenaltyDerivativeOrder = 1;
  208.         int iCurvaturePenaltyDerivativeOrder = 2;

  210.         SegmentInelasticDesignControl sdic = new SegmentInelasticDesignControl (
  211.             iK,
  212.             new org.drip.spline.params.SegmentFlexurePenaltyControl (
  213.                 iLengthPenaltyDerivativeOrder,
  214.                 dblLengthPenaltyAmplitude
  215.             ),
  216.             new org.drip.spline.params.SegmentFlexurePenaltyControl (
  217.                 iCurvaturePenaltyDerivativeOrder,
  218.                 dblCurvaturePenaltyAmplitude
  219.             )
  220.         );

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

  224.         System.out.println (" \n         == ORIGINAL #1 ==      $$   == ORIGINAL #2 ==    $$   == BEST FIT ==    ");

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

  228.         int iPolyNumBasis = 4;

  230.         /* 
  231.          * Construct the base, the base + 1 degree segment builder control
  232.          */

  234.         SegmentCustomBuilderControl scbc1 = PolynomialSegmentControlParams (
  235.             iPolyNumBasis,
  236.             sdic,
  237.             rssc
  238.         );

  240.         SegmentCustomBuilderControl scbc2 = PolynomialSegmentControlParams (
  241.             iPolyNumBasis + 1,
  242.             sdic,
  243.             rssc
  244.         );

  246.         /* 
  247.          * Construct the base, the elevated, and the best fit basis spline stretches
  248.          */

  250.         MultiSegmentSequence mssBase1 = BasisSplineStretchTest (
  251.             adblX,
  252.             adblY,
  253.             scbc1,
  254.             null
  255.         );

  257.         MultiSegmentSequence mssBase2 = BasisSplineStretchTest (
  258.             adblX,
  259.             adblY,
  260.             scbc2,
  261.             null
  262.         );

  264.         MultiSegmentSequence mssBestFit = BasisSplineStretchTest (
  265.             adblX,
  266.             adblY,
  267.             scbc2,
  268.             rbfr
  269.         );

  271.         /*
  272.          * Compute the segment-by-segment response and monotonicity for all the three stretches
  273.          */

  275.         double dblX = mssBase1.getLeftPredictorOrdinateEdge();

  277.         double dblXMax = mssBase1.getRightPredictorOrdinateEdge();

  279.         while (dblX <= dblXMax) {
  280.             System.out.println (
  281.                 "Y[" + FormatUtil.FormatDouble (dblX, 1, 2, 1.) + "] " +
  282.                 FormatUtil.FormatDouble (mssBase1.responseValue (dblX), 2, 2, 1.) + " | "
  283.                     + mssBase1.monotoneType (dblX) + " $$ "
  284.                 + FormatUtil.FormatDouble (mssBase2.responseValue (dblX), 2, 2, 1.) + " | "
  285.                     + mssBase2.monotoneType (dblX) + " $$ "
  286.                 + FormatUtil.FormatDouble (mssBestFit.responseValue (dblX), 2, 2, 1.) + " | "
  287.                     + mssBestFit.monotoneType (dblX));

  289.             dblX += 0.25;
  290.         }

  292.         /*
  293.          * Compute the Stretch Jacobian for all the three stretches
  294.          */

  296.         dblX = mssBase1.getLeftPredictorOrdinateEdge();

  298.         while (dblX <= dblXMax) {
  299.             System.out.println (
  300.                 "\t\tJacobian Y[" + FormatUtil.FormatDouble (dblX, 2, 2, 1.) + "] => " +
  301.                     mssBase1.jackDResponseDCalibrationInput (dblX, 1).displayString());

  303.             System.out.println (
  304.                 "\t\tJacobian Y[" + FormatUtil.FormatDouble (dblX, 2, 2, 1.) + "] => " +
  305.                     mssBase2.jackDResponseDCalibrationInput (dblX, 1).displayString());

  307.             System.out.println (
  308.                 "\t\tJacobian Y[" + FormatUtil.FormatDouble (dblX, 2, 2, 1.) + "] => " +
  309.                     mssBestFit.jackDResponseDCalibrationInput (dblX, 1).displayString());

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

  313.             dblX += 0.25;
  314.         }

  316.         /*
  317.          * Compute the Base Stretch Curvature, Length, and the Best Fit DPE
  318.          */

  320.         System.out.println ("\n\t\t----STRETCH #1----\n\t\t-----------------");

  322.         System.out.println ("\tCURVATURE DPE         => " +
  323.             FormatUtil.FormatDouble (mssBase1.curvatureDPE(), 10, 0, 1.));

  325.         System.out.println ("\tLENGTH DPE            => " +
  326.             FormatUtil.FormatDouble (mssBase1.lengthDPE(), 10, 0, 1.));

  328.         System.out.println ("\tBEST FIT DPE          => " +
  329.             FormatUtil.FormatDouble (mssBase1.bestFitDPE (rbfr), 10, 0, 1.));

  331.         /*
  332.          * Compute the Elevated Stretch Curvature, Length, and the Best Fit DPE
  333.          */

  335.         System.out.println ("\n\t\t----STRETCH #2----\n\t\t-----------------");

  337.         System.out.println ("\tCURVATURE DPE         => " +
  338.             FormatUtil.FormatDouble (mssBase2.curvatureDPE(), 10, 0, 1.));

  340.         System.out.println ("\tLENGTH DPE            => " +
  341.             FormatUtil.FormatDouble (mssBase2.lengthDPE(), 10, 0, 1.));

  343.         System.out.println ("\tBEST FIT DPE          => " +
  344.             FormatUtil.FormatDouble (mssBase2.bestFitDPE (rbfr), 10, 0, 1.));

  346.         /*
  347.          * Compute the Best Fit Stretch Curvature, Length, and the Best Fit DPE
  348.          */

  350.         System.out.println ("\n\t\t----STRETCH BEST FIT----\n\t\t-----------------------");

  352.         System.out.println ("\tCURVATURE DPE         => " +
  353.             FormatUtil.FormatDouble (mssBestFit.curvatureDPE(), 10, 0, 1.));

  355.         System.out.println ("\tLENGTH DPE            => " +
  356.             FormatUtil.FormatDouble (mssBestFit.lengthDPE(), 10, 0, 1.));

  358.         System.out.println ("\tBEST FIT DPE          => " +
  359.             FormatUtil.FormatDouble (mssBestFit.bestFitDPE (rbfr), 10, 0, 1.));
  360.     }

  362.     public static final void main (
  363.         final String[] astrArgs)
  364.         throws Exception
  365.     {
  366.         PenalizedCurvatureLengthFitTest();
  367.     }
  368. }
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