BasisSplineSet.java
package org.drip.sample.spline;
import org.drip.function.r1tor1.*;
import org.drip.numerical.differentiation.WengertJacobian;
import org.drip.spline.basis.*;
import org.drip.spline.params.*;
import org.drip.spline.segment.*;
/*
* -*- 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.
*/
/**
* BasisSplineSet implements Samples for the Construction and the usage of various basis spline functions. It
* demonstrates the following:
* - Construction of segment control parameters - polynomial (regular/Bernstein) segment control,
* exponential/hyperbolic tension segment control, Kaklis-Pandelis tension segment control, and C1
* Hermite.
* - Control the segment using the rational shape controller, and the appropriate Ck.
* - Estimate the node value and the node value Jacobian with the segment, as well as at the boundaries.
* - Calculate the segment monotonicity.
* @author Lakshmi Krishnamurthy
*/
public class BasisSplineSet {
/*
* Sample demonstrating the creation of the polynomial basis spline set
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final FunctionSet CreatePolynomialSpline()
throws Exception
{
int iNumBasis = 4;
/*
* Create the basis parameter set from the number of basis functions, and construct the basis
*/
PolynomialFunctionSetParams polybsbp = new PolynomialFunctionSetParams (iNumBasis);
return FunctionSetBuilder.PolynomialBasisSet (polybsbp);
}
/*
* Sample demonstrating the creation of the Bernstein polynomial basis spline set
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final FunctionSet CreateBernsteinPolynomialSpline()
throws Exception
{
int iNumBasis = 4;
/*
* Create the basis parameter set from the number of basis functions, and construct the basis
*/
PolynomialFunctionSetParams polybsbp = new PolynomialFunctionSetParams (iNumBasis);
return FunctionSetBuilder.BernsteinPolynomialBasisSet (polybsbp);
}
/*
* Sample demonstrating the creation of the exponential tension basis spline set
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final FunctionSet CreateExponentialTensionSpline()
throws Exception
{
double dblTension = 1.;
/*
* Create the basis parameter set from the segment tension parameter, and construct the basis
*/
ExponentialTensionSetParams etbsbp = new ExponentialTensionSetParams (dblTension);
return FunctionSetBuilder.ExponentialTensionBasisSet (etbsbp);
}
/*
* Sample demonstrating the creation of the hyperbolic tension basis spline set
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final FunctionSet CreateHyperbolicTensionSpline()
throws Exception
{
double dblTension = 1.;
/*
* Create the basis parameter set from the segment tension parameter, and construct the basis
*/
ExponentialTensionSetParams etbsbp = new ExponentialTensionSetParams (dblTension);
return FunctionSetBuilder.HyperbolicTensionBasisSet (etbsbp);
}
/*
* Sample demonstrating the creation of the Kaklis Pandelis basis spline set
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final FunctionSet CreateKaklisPandelisSpline()
throws Exception
{
int iPolynomialTensionDegree = 2;
/*
* Create the basis parameter set from the segment polynomial tension control, and construct the basis
*/
KaklisPandelisSetParams kpbpsp = new KaklisPandelisSetParams (iPolynomialTensionDegree);
return FunctionSetBuilder.KaklisPandelisBasisSet (kpbpsp);
}
/*
* This sample demonstrates the following:
*
* - Construction of two segments, 1 and 2.
* - Calibration of the segments to the left and the right node values
* - Extraction of the segment Jacobians and segment monotonicity
* - Estimate point value and the Jacobian
* - Estimate the curvature penalty
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final void TestSpline (
final FunctionSet fs,
final ResponseScalingShapeControl rssc,
final SegmentInelasticDesignControl segParams)
throws Exception
{
/*
* Construct the left and the right segments
*/
LatentStateResponseModel seg1 = LatentStateResponseModel.Create (
1.0,
1.5,
fs,
rssc,
segParams
);
LatentStateResponseModel seg2 = LatentStateResponseModel.Create (
1.5,
2.0,
fs,
rssc,
segParams
);
/*
* Calibrate the left segment using the node values, and compute the segment Jacobian, monotonicity, and curvature penalty
*/
WengertJacobian wj1 = seg1.jackDCoeffDEdgeParams (
25.,
0.,
20.25,
null
);
System.out.println ("\tY[" + 1.0 + "]: " + seg1.responseValue (1.));
System.out.println ("\tY[" + 1.5 + "]: " + seg1.responseValue (1.5));
System.out.println ("Segment 1 Jacobian: " + wj1.displayString());
System.out.println ("Segment 1 Head: " + seg1.jackDCoeffDEdgeInputs().displayString());
System.out.println ("Segment 1 Monotone Type: " + seg1.monotoneType());
System.out.println ("Segment 1 DPE: " + seg1.curvatureDPE());
/*
* Calibrate the right segment using the node values, and compute the segment Jacobian, monotonicity, and curvature penalty
*/
WengertJacobian wj2 = seg2.jackDCoeffDEdgeParams (
seg1,
"Default",
16.,
null,
Double.NaN,
null
);
System.out.println ("\tY[" + 1.5 + "]: " + seg2.responseValue (1.5));
System.out.println ("\tY[" + 2. + "]: " + seg2.responseValue (2.));
System.out.println ("Segment 2 Jacobian: " + wj2.displayString());
System.out.println ("Segment 2 Regular Jacobian: " + seg2.jackDCoeffDEdgeInputs().displayString());
System.out.println ("Segment 2 Monotone Type: " + seg2.monotoneType());
System.out.println ("Segment 2 DPE: " + seg2.curvatureDPE());
/*
* Re-calibrate Segment #2 with a different response value
*/
seg2.calibrate (
seg1,
14.,
null
);
/*
* Estimate the segment value at the given variate, and compute the corresponding Jacobian and curvature penalty
*/
double dblX = 2.0;
System.out.println ("\t\tValue[" + dblX + "]: " + seg2.responseValue (dblX));
System.out.println ("\t\tValue Jacobian[" + dblX + "]: " + seg2.jackDResponseDEdgeInput (dblX, 1).displayString());
System.out.println ("\t\tSegment 2 DPE: " + seg2.curvatureDPE());
}
/*
* This sample demonstrates the following specifically for the C1 Hermite Splines, which are calibrated
* using left and right node values, along with their derivatives:
*
* - Construction of two segments, 1 and 2.
* - Calibration of the segments to the left and the right node values
* - Extraction of the segment Jacobians and segment monotonicity
* - Estimate point value and the Jacobian
* - Estimate the curvature penalty
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final void TestC1HermiteSpline (
final FunctionSet fs,
final ResponseScalingShapeControl sc,
final SegmentInelasticDesignControl segParams)
throws Exception
{
/*
* Construct the left and the right segments
*/
LatentStateResponseModel seg1 = LatentStateResponseModel.Create (
0.0,
1.0,
fs,
sc,
segParams
);
LatentStateResponseModel seg2 = LatentStateResponseModel.Create (
1.0,
2.0,
fs,
sc,
segParams
);
/*
* Calibrate the left segment using the node values, and compute the segment Jacobian, monotonicity, and curvature penalty
*/
WengertJacobian wj1 = seg1.jackDCoeffDEdgeParams (
new double[] {0., 1.}, // Left/Right X
new double[] {1., 4.}, // Left/Right Y
new double[] {1.}, // Left Deriv
new double[] {6.}, // Right Deriv
null,
null // Constraints, Fitness Weighted Response
);
System.out.println ("\tY[" + 0.0 + "]: " + seg1.responseValue (0.0));
System.out.println ("\tY[" + 1.0 + "]: " + seg1.responseValue (1.0));
System.out.println ("Segment 1 Jacobian: " + wj1.displayString());
System.out.println ("Segment 1 Head: " + seg1.jackDCoeffDEdgeInputs().displayString());
System.out.println ("Segment 1 Monotone Type: " + seg1.monotoneType());
System.out.println ("Segment 1 DPE: " + seg1.curvatureDPE());
/*
* Calibrate the right segment using the node values, and compute the segment Jacobian, monotonicity, and curvature penalty
*/
WengertJacobian wj2 = seg2.jackDCoeffDEdgeParams (
new double[] {1., 2.}, // Left/Right X
new double[] {4., 15.}, // Left/Right Y
new double[] {6.}, // Left Deriv
new double[] {17.}, // Right Deriv
null,
null // Constraints, Fitness Weighted Response
);
System.out.println ("\tY[" + 1.0 + "]: " + seg2.responseValue (1.0));
System.out.println ("\tY[" + 2.0 + "]: " + seg2.responseValue (2.0));
System.out.println ("Segment 2 Jacobian: " + wj2.displayString());
System.out.println ("Segment 2 Regular Jacobian: " + seg2.jackDCoeffDEdgeInputs().displayString());
System.out.println ("Segment 2 Monotone Type: " + seg2.monotoneType());
System.out.println ("Segment 2 DPE: " + seg2.curvatureDPE());
/*
* Re-calibrate Segment #2 with a different response value
*/
seg2.calibrate (
seg1,
14.,
null
);
/*
* Estimate the segment value at the given variate, and compute the corresponding Jacobian, monotonicity, and curvature penalty
*/
double dblX = 2.0;
System.out.println ("\t\tValue[" + dblX + "]: " + seg2.responseValue (dblX));
System.out.println ("\t\tValue Jacobian[" + dblX + "]: " + seg2.jackDResponseDEdgeInput (dblX, 1).displayString());
System.out.println ("\t\tSegment 2 DPE: " + seg2.curvatureDPE());
}
/*
* This sample illustrates the construction and the usage of basis splines (all types, really). It shows
* the following:
* - Construct a rational shape controller with the specified shape controller tension.
* - Construct the segment inelastic parameter that is C2 (iK = 2 sets it to C2), with second order
* curvature penalty, and without constraint.
* - Test the polynomial basis spline.
* - Test the Bernstein polynomial basis spline.
* - Test the exponential tension basis spline.
* - Test the hyperbolic tension basis spline.
* - Test the Kaklis-Pandelis basis spline.
* - Test the C1 Hermite basis spline.
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final void BasisSplineSetSample()
throws Exception
{
/*
* Construct a rational shape controller with the shape controller tension of 1.
*/
double dblShapeControllerTension = 1.;
ResponseScalingShapeControl rssc = new ResponseScalingShapeControl (
true,
new QuadraticRationalShapeControl (dblShapeControllerTension)
);
/*
* Construct the segment inelastic parameter that is C2 (iK = 2 sets it to C2), with second order
* curvature penalty, and without constraint
*/
int iK = 2;
int iCurvaturePenaltyDerivativeOrder = 2;
SegmentInelasticDesignControl segParams = SegmentInelasticDesignControl.Create (
iK,
iCurvaturePenaltyDerivativeOrder
);
/*
* Test the polynomial spline
*/
System.out.println (" ---------- \n POLYNOMIAL \n ---------- \n");
TestSpline (
CreatePolynomialSpline(),
null,
segParams
);
/*
* Test the Bernstein polynomial spline
*/
System.out.println (" -------------------- \n BERNSTEINPOLYNOMIAL \n -------------------- \n");
TestSpline (
CreateBernsteinPolynomialSpline(),
rssc,
segParams
);
/*
* Test the exponential tension spline
*/
System.out.println ( " ----------- \n EXPONENTIAL \n ----------- \n");
TestSpline (
CreateExponentialTensionSpline(),
rssc,
segParams
);
/*
* Test the hyperbolic tension spline
*/
System.out.println (" ---------- \n HYPERBOLIC \n ---------- \n");
TestSpline (
CreateHyperbolicTensionSpline(),
rssc,
segParams
);
/*
* Test the Kaklis-Pandelis spline
*/
System.out.println (" -------------------- \n KAKLISPANDELIS \n -------------------- \n");
TestSpline (
CreateKaklisPandelisSpline(),
rssc,
segParams
);
/*
* Test the C1 Hermite spline
*/
System.out.println (" -------------------- \n C1 HERMITE \n -------------------- \n");
TestC1HermiteSpline (
CreatePolynomialSpline(),
rssc,
SegmentInelasticDesignControl.Create (
1,
iCurvaturePenaltyDerivativeOrder
)
);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
BasisSplineSetSample();
}
}