BasisMulticBSpline.java
package org.drip.sample.spline;
import org.drip.numerical.common.FormatUtil;
import org.drip.spline.bspline.*;
/*
* -*- 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.
*/
/**
* BasisMulticBSpline implements Samples for the Construction and the usage of various multic basis B Splines.
* It demonstrates the following:
* - Construction of segment higher order B Spline from the corresponding Hat Basis Functions.
* - Estimation of the derivatives and the basis envelope cumulative integrands.
* - Estimation of the normalizer and the basis envelope cumulative normalized integrands.
*
* @author Lakshmi Krishnamurthy
*/
public class BasisMulticBSpline {
/*
* This sample illustrates the construction and the usage of multic basis functions, and their eventual
* response/derivative computation and comparison with the corresponding raw/processed and monic basis.
* It shows the following:
* - Construct the hyperbolic tension basis hat pair using the left predictor ordinates and the tension.
* - Construct the hyperbolic tension basis hat pair using the right predictor ordinates and the
* tension.
* - Generate the left monic basis function from the hat type, left predictor ordinates, shape control,
* and the tension parameters.
* - Generate the right monic basis function from the hat type, right predictor ordinates, shape
* control, and the tension parameters.
* - Run a response value calculation comparison across the predictor ordinates for each of the left
* basis hat and the monic basis functions.
* - Run a response value calculation comparison across the predictor ordinates for each of the right
* basis hat and the monic basis functions.
* - Construct a multic basis function using the left/right monic basis functions, and the multic order.
* - Display the multic Basis Function response as well as normalized Cumulative across the specified
* variate range.
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final void RunMulticBSplineTest (
final String strHatType,
final String strShapeControlType,
final double dblTension,
final int iMulticBSplineOrder)
throws Exception
{
double[] adblPredictorOrdinateLeft = new double[] {
1., 2., 3.
};
double[] adblPredictorOrdinateRight = new double[] {
2., 3., 4.
};
/*
* Construct the hyperbolic tension basis hat pair using the left predictor ordinates and the
* tension.
*/
TensionBasisHat[] aTBHLeft = BasisHatPairGenerator.HyperbolicTensionHatPair (
adblPredictorOrdinateLeft[0],
adblPredictorOrdinateLeft[1],
adblPredictorOrdinateLeft[2],
dblTension
);
/*
* Construct the hyperbolic tension basis hat pair using the right predictor ordinates and the
* tension.
*/
TensionBasisHat[] aTBHRight = BasisHatPairGenerator.HyperbolicTensionHatPair (
adblPredictorOrdinateRight[0],
adblPredictorOrdinateRight[1],
adblPredictorOrdinateRight[2],
dblTension
);
/*
* Generate the left monic basis function from the hat type, left predictor ordinates, shape control,
* and the tension parameters.
*/
SegmentBasisFunction sbfMonicLeft = SegmentBasisFunctionGenerator.Monic (
strHatType,
strShapeControlType,
adblPredictorOrdinateLeft,
2,
dblTension
);
/*
* Generate the right monic basis function from the hat type, right predictor ordinates, shape
* control, and the tension parameters.
*/
SegmentBasisFunction sbfMonicRight = SegmentBasisFunctionGenerator.Monic (
strHatType,
strShapeControlType,
adblPredictorOrdinateRight,
2,
dblTension
);
/*
* Run a response value calculation comparison across the predictor ordinates for each of the left
* basis hat and the monic basis functions.
*/
System.out.println ("\n\t-------------------------------------------------");
System.out.println ("\t X | LEFT | RIGHT | MONIC ");
System.out.println ("\t-------------------------------------------------");
double dblX = 0.50;
double dblXIncrement = 0.25;
while (dblX <= 4.50) {
System.out.println (
"\tResponse[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
FormatUtil.FormatDouble (aTBHLeft[0].evaluate (dblX), 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (aTBHLeft[1].evaluate (dblX), 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (sbfMonicLeft.evaluate (dblX), 1, 5, 1.)
);
dblX += dblXIncrement;
}
/*
* Run a response value calculation comparison across the predictor ordinates for each of the right
* basis hat and the monic basis functions.
*/
System.out.println ("\n\t-------------------------------------------------");
System.out.println ("\t X | LEFT | RIGHT | MONIC ");
System.out.println ("\t-------------------------------------------------");
dblX = 0.50;
while (dblX <= 4.50) {
System.out.println (
"\tResponse[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
FormatUtil.FormatDouble (aTBHRight[0].evaluate (dblX), 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (aTBHRight[1].evaluate (dblX), 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (sbfMonicRight.evaluate (dblX), 1, 5, 1.)
);
dblX += dblXIncrement;
}
/*
* Construct a multic basis function using the left/right monic basis functions, and the multic
* order.
*/
SegmentBasisFunction[] sbfMultic = SegmentBasisFunctionGenerator.MulticSequence (
iMulticBSplineOrder,
new SegmentBasisFunction[] {
sbfMonicLeft,
sbfMonicRight
}
);
/*
* Display the multic Basis Function response as well as normalized Cumulative across the specified
* variate range.
*/
System.out.println ("\n\t-------------------------------------------------");
System.out.println ("\t PREDICTOR | RESPONSE | CUMULATIVE ");
System.out.println ("\t-------------------------------------------------");
dblX = 0.50;
dblXIncrement = 0.125;
while (dblX <= 4.50) {
System.out.println (
"\t\tMultic[" + FormatUtil.FormatDouble (dblX, 1, 3, 1.) + "] : " +
FormatUtil.FormatDouble (sbfMultic[0].evaluate (dblX), 1, 5, 1.) + " | " +
FormatUtil.FormatDouble (sbfMultic[0].normalizedCumulative (dblX), 1, 5, 1.)
);
dblX += dblXIncrement;
}
System.out.println ("\n\t-------------------------------------------------\n");
}
/*
* This sample illustrates a sequence of tests using basis multic B Splines. In particular it shows the
* following:
* - Creation and usage of Multic B Spline built off of raw hyperbolic tension basis function, rational
* linear shape controller, tension = 1.0, and 3rd order multic.
* - Creation and usage of Multic B Spline built off of processed hyperbolic tension basis function,
* rational linear shape controller, tension = 1.0, and 3rd order multic.
* - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* linear shape controller, tension = 0.0, and 3rd order multic.
* - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* linear shape controller, tension = 1.0, and 3rd order multic.
* - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* quadratic shape controller, tension = 1.0, and 3rd order multic.
* - Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* exponential shape controller, tension = 1.0, and 3rd order multic.
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final void BasisMulticBSplineSample()
throws Exception
{
/*
* Creation and usage of Multic B Spline built off of raw hyperbolic tension basis function,
* rational linear shape controller, tension = 1.0, and 3rd order multic.
*/
System.out.println ("\n RAW TENSION HYPERBOLIC | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.RAW_TENSION_HYPERBOLIC,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
1.,
3
);
/*
* Creation and usage of Multic B Spline built off of processed hyperbolic tension basis function,
* rational linear shape controller, tension = 1.0, and 3rd order multic.
*/
System.out.println ("\n PROC TENSION HYPERBOLIC | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.PROCESSED_TENSION_HYPERBOLIC,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
1.,
3
);
/*
* Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* linear shape controller, tension = 0.0, and 3rd order multic.
*/
System.out.println ("\n RAW CUBIC RATIONAL | LINEAR SHAPE CONTROL | TENSION = 0.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
0.,
3
);
/*
* Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* linear shape controller, tension = 1.0, and 3rd order multic.
*/
System.out.println ("\n RAW CUBIC RATIONAL | LINEAR SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_LINEAR,
1.,
3
);
/*
* Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* quadratic shape controller, tension = 1.0, and 3rd order multic.
*/
System.out.println ("\n RAW CUBIC RATIONAL | QUADRATIC SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_QUADRATIC,
1.,
3
);
/*
* Creation and usage of Multic B Spline built off of raw cubic tension basis function, rational
* exponential shape controller, tension = 1.0, and 3rd order multic.
*/
System.out.println ("\n RAW CUBIC RATIONAL | EXPONENTIAL SHAPE CONTROL | TENSION = 1.0 | CUBIC B SPLINE");
RunMulticBSplineTest (
BasisHatPairGenerator.PROCESSED_CUBIC_RATIONAL,
BasisHatShapeControl.SHAPE_CONTROL_RATIONAL_EXPONENTIAL,
1.,
3
);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
BasisMulticBSplineSample();
}
}