CurvatureRoughnessPenaltyFit.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.  * CurvatureRoughnessPenaltyFit demonstrates the setting up and the usage of the curvature and closeness of
  61.  *  fit penalizing spline. It illustrates in detail the following steps:
  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 2nd order roughness
  68.  *      penalty derivative, and without constraint.
  69.  *  - Construct the base, the base + 1 degree segment builder control.
  70.  *  - Construct the base, the elevated, and the best fit basis spline stretches.
  71.  *  - Compute the segment-by-segment monotonicity for all the three stretches.
  72.  *  - Compute the Stretch Jacobian for all the three stretches.
  73.  *  - Compute the Base Stretch Curvature Penalty Estimate.
  74.  *  - Compute the Elevated Stretch Curvature Penalty Estimate.
  75.  *  - Compute the Best Fit Stretch Curvature Penalty Estimate.
  76.  *
  77.  * @author Lakshmi Krishnamurthy
  78.  */

  80. public class CurvatureRoughnessPenaltyFit {

  82.     /*
  83.      * Build Polynomial Segment Control Parameters
  84.      * 
  85.      *  WARNING: Insufficient Error Checking, so use caution
  86.      */

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

  103.     /*
  104.      * Construct the Basis Spline Stretch Instance using the following inputs:
  105.      *  - Array of Segment Builder Parameters - one per segment
  106.      *  - Construct a Calibrated Stretch instance
  107.      * 
  108.      *  WARNING: Insufficient Error Checking, so use caution
  109.      */

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

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

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

  127.         /*
  128.          * Construct a Calibrated Stretch instance 
  129.          */

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

  142.     /*
  143.      * Bring it all together in the Penalized Curvature Fit Test using the following steps:
  144.      *  - Set up the X Predictor Ordinate and the Y Response Value Set.
  145.      *  - Construct a set of Predictor Ordinates, their Responses, and corresponding Weights to serve as
  146.      *      weighted closeness of fit.
  147.      *  - Construct a rational shape controller with the desired shape controller tension parameters and Global Scaling.
  148.      *  - Construct the segment inelastic parameter that is C2 (iK = 2 sets it to C2), with 2nd order
  149.      *      roughness penalty derivative, and without constraint.
  150.      *  - Construct the base, the base + 1 degree segment builder control.
  151.      *  - Construct the base, the elevated, and the best fit basis spline stretches.
  152.      *  - Compute the segment-by-segment monotonicity for all the three stretches.
  153.      *  - Compute the Stretch Jacobian for all the three stretches.
  154.      *  - Compute the Base Stretch Curvature Penalty Estimate.
  155.      *  - Compute the Elevated Stretch Curvature Penalty Estimate.
  156.      *  - Compute the Best Fit Stretch Curvature Penalty Estimate.
  157.      */

  159.     public static final void PenalizedCurvatureFitTest()
  160.         throws Exception
  161.     {
  162.         /*
  163.          * X predictors
  164.          */

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

  168.         /*
  169.          * Y responses
  170.          */

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

  174.         /*
  175.          * Construct a set of Predictor Ordinates, their Responses, and corresponding Weights to serve as
  176.          *  weighted closeness of fit.
  177.          */

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

  185.         /*
  186.          * Construct a rational shape controller with the shape controller tension of 1, and Global Scaling.
  187.          */

  189.         double dblShapeControllerTension = 1.;

  191.         ResponseScalingShapeControl rssc = new ResponseScalingShapeControl (
  192.             false,
  193.             new QuadraticRationalShapeControl (dblShapeControllerTension)
  194.         );

  196.         /*
  197.          * Construct the segment inelastic parameter that is C2 (iK = 2 sets it to C2), with 2nd order
  198.          *  roughness penalty derivative, and without constraint
  199.          */

  201.         int iK = 2;
  202.         int iRoughnessPenaltyDerivativeOrder = 2;

  204.         SegmentInelasticDesignControl sdic = SegmentInelasticDesignControl.Create (
  205.             iK,
  206.             iRoughnessPenaltyDerivativeOrder
  207.         );

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

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

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

  215.         int iPolyNumBasis = 4;

  217.         /* 
  218.          * Construct the base, the base + 1 degree segment builder control
  219.          */

  221.         SegmentCustomBuilderControl scbc1 = PolynomialSegmentControlParams (
  222.             iPolyNumBasis,
  223.             sdic,
  224.             rssc
  225.         );

  227.         SegmentCustomBuilderControl scbc2 = PolynomialSegmentControlParams (
  228.             iPolyNumBasis + 1,
  229.             sdic,
  230.             rssc
  231.         );

  233.         /* 
  234.          * Construct the base, the elevated, and the best fit basis spline stretches
  235.          */

  237.         MultiSegmentSequence mssBase1 = BasisSplineStretchTest (
  238.             adblX,
  239.             adblY,
  240.             scbc1,
  241.             null
  242.         );

  244.         MultiSegmentSequence mssBase2 = BasisSplineStretchTest (
  245.             adblX,
  246.             adblY,
  247.             scbc2,
  248.             null
  249.         );

  251.         MultiSegmentSequence mssBestFit = BasisSplineStretchTest (
  252.             adblX,
  253.             adblY,
  254.             scbc2,
  255.             sbfr
  256.         );

  258.         /*
  259.          * Compute the segment-by-segment monotonicity for all the three stretches
  260.          */

  262.         double dblX = mssBase1.getLeftPredictorOrdinateEdge();

  264.         double dblXMax = mssBase1.getRightPredictorOrdinateEdge();

  266.         while (dblX <= dblXMax) {
  267.             System.out.println (
  268.                 "Y[" + FormatUtil.FormatDouble (dblX, 1, 2, 1.) + "] " +
  269.                 FormatUtil.FormatDouble (mssBase1.responseValue (dblX), 2, 2, 1.) + " | "
  270.                     + mssBase1.monotoneType (dblX) + " $$ "
  271.                 + FormatUtil.FormatDouble (mssBase2.responseValue (dblX), 2, 2, 1.) + " | "
  272.                     + mssBase2.monotoneType (dblX) + " $$ "
  273.                 + FormatUtil.FormatDouble (mssBestFit.responseValue (dblX), 2, 2, 1.) + " | "
  274.                     + mssBestFit.monotoneType (dblX));

  276.             dblX += 0.25;
  277.         }

  279.         /*
  280.          * Compute the Stretch Jacobian for all the three stretches
  281.          */

  283.         dblX = mssBase1.getLeftPredictorOrdinateEdge();

  285.         while (dblX <= dblXMax) {
  286.             System.out.println (
  287.                 "\t\tJacobian Y[" + FormatUtil.FormatDouble (dblX, 2, 2, 1.) + "] => " +
  288.                     mssBase1.jackDResponseDCalibrationInput (dblX, 1).displayString());

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

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

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

  300.             dblX += 0.25;
  301.         }

  303.         /*
  304.          * Compute the Base Stretch Curvature Penalty Estimate
  305.          */

  307.         System.out.println ("\tBASE #1  DPE: " + FormatUtil.FormatDouble (mssBase1.curvatureDPE(), 10, 0, 1.));

  309.         /*
  310.          * Compute the Elevated Stretch Curvature Penalty Estimate
  311.          */

  313.         System.out.println ("\tBASE #2  DPE: " + FormatUtil.FormatDouble (mssBase2.curvatureDPE(), 10, 0, 1.));

  315.         /*
  316.          * Compute the Best Fit Stretch Curvature Penalty Estimate
  317.          */

  319.         System.out.println ("\tBEST FIT DPE: " + FormatUtil.FormatDouble (mssBestFit.curvatureDPE(), 10, 0, 1.));
  320.     }

  322.     public static final void main (
  323.         final String[] astrArgs)
  324.         throws Exception
  325.     {
  326.         PenalizedCurvatureFitTest();
  327.     }
  328. }
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