BestFitFlexurePenalizer.java
package org.drip.spline.segment;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* 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 DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* 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.
*/
/**
* <i>BestFitFlexurePenalizer</i> implements the Segment's Best Fit, Curvature, and Length Penalizers. It
* provides the following functionality:
*
* <br><br>
* <ul>
* <li>
* Compute the Cross-Curvature Penalty for the given Basis Pair
* </li>
* <li>
* Compute the Cross-Length Penalty for the given Basis Pair
* </li>
* <li>
* Compute the Best Fit Cross-Product Penalty for the given Basis Pair
* </li>
* <li>
* Compute the Basis Pair Penalty Coefficient for the Best Fit and the Curvature Penalties
* </li>
* <li>
* Compute the Penalty Constraint for the Basis Pair
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/SplineBuilderLibrary.md">Spline Builder Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/README.md">Basis Splines and Linear Compounders across a Broad Family of Spline Basis Functions</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spline/segment/README.md">Flexure Penalizing Best Fit Segment</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class BestFitFlexurePenalizer {
private org.drip.spline.segment.BasisEvaluator _lbe = null;
private org.drip.spline.segment.LatentStateInelastic _ics = null;
private org.drip.spline.params.SegmentBestFitResponse _sbfr = null;
private org.drip.spline.params.SegmentFlexurePenaltyControl _sfpcLength = null;
private org.drip.spline.params.SegmentFlexurePenaltyControl _sfpcCurvature = null;
/**
* BestFitFlexurePenalizer constructor
*
* @param ics Segment Inelastics
* @param sfpcCurvature Curvature Penalty Parameters
* @param sfpcLength Length Penalty Parameters
* @param sbfr Best Fit Weighted Response
* @param lbe The Local Basis Evaluator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public BestFitFlexurePenalizer (
final org.drip.spline.segment.LatentStateInelastic ics,
final org.drip.spline.params.SegmentFlexurePenaltyControl sfpcCurvature,
final org.drip.spline.params.SegmentFlexurePenaltyControl sfpcLength,
final org.drip.spline.params.SegmentBestFitResponse sbfr,
final org.drip.spline.segment.BasisEvaluator lbe)
throws java.lang.Exception
{
if (null == (_lbe = lbe) || null == (_ics = ics))
throw new java.lang.Exception ("BestFitFlexurePenalizer ctr: Invalid Inputs");
_sbfr = sbfr;
_sfpcLength = sfpcLength;
_sfpcCurvature = sfpcCurvature;
}
/**
* Compute the Cross-Curvature Penalty for the given Basis Pair
*
* @param iBasisIndexI I Basis Index (I is the Summation Index)
* @param iBasisIndexR R Basis Index (R is the Separator Index)
*
* @return The Cross-Curvature Penalty for the given Basis Pair
*
* @throws java.lang.Exception Thrown if the Cross-Curvature Penalty cannot be computed
*/
public double basisPairCurvaturePenalty (
final int iBasisIndexI,
final int iBasisIndexR)
throws java.lang.Exception
{
if (null == _sfpcCurvature) return 0.;
org.drip.function.definition.R1ToR1 au = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblVariate)
throws Exception
{
int iOrder = _sfpcCurvature.derivativeOrder();
return _lbe.shapedBasisFunctionDerivative (dblVariate, iOrder, iBasisIndexI) *
_lbe.shapedBasisFunctionDerivative (dblVariate, iOrder, iBasisIndexR);
}
@Override public double integrate (
final double dblBegin,
final double dblEnd)
throws java.lang.Exception
{
return org.drip.numerical.integration.R1ToR1Integrator.Boole (this, dblBegin, dblEnd);
}
};
return _sfpcCurvature.amplitude() * au.integrate (_ics.left(), _ics.right());
}
/**
* Compute the Cross-Length Penalty for the given Basis Pair
*
* @param iBasisIndexI I Basis Index (I is the Summation Index)
* @param iBasisIndexR R Basis Index (R is the Separator Index)
*
* @return The Cross-Length Penalty for the given Basis Pair
*
* @throws java.lang.Exception Thrown if the Cross-Length Penalty cannot be computed
*/
public double basisPairLengthPenalty (
final int iBasisIndexI,
final int iBasisIndexR)
throws java.lang.Exception
{
if (null == _sfpcLength) return 0.;
org.drip.function.definition.R1ToR1 au = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblVariate)
throws Exception
{
int iOrder = _sfpcLength.derivativeOrder();
return _lbe.shapedBasisFunctionDerivative (dblVariate, iOrder, iBasisIndexI) *
_lbe.shapedBasisFunctionDerivative (dblVariate, iOrder, iBasisIndexR);
}
@Override public double integrate (
final double dblBegin,
final double dblEnd)
throws java.lang.Exception
{
return org.drip.numerical.integration.R1ToR1Integrator.Boole (this, dblBegin, dblEnd);
}
};
return _sfpcLength.amplitude() * au.integrate (_ics.left(), _ics.right());
}
/**
* Compute the Best Fit Cross-Product Penalty for the given Basis Pair
*
* @param iBasisIndexI I Basis Index (I is the Summation Index)
* @param iBasisIndexR R Basis Index (R is the Separator Index)
*
* @return The Best Fit Cross-Product Penalty for the given Basis Pair
*
* @throws java.lang.Exception Thrown if the Best Fit Cross-Product Penalty cannot be computed
*/
public double basisBestFitPenalty (
final int iBasisIndexI,
final int iBasisIndexR)
throws java.lang.Exception
{
if (null == _sbfr) return 0.;
int iNumPoint = _sbfr.numPoint();
if (0 == iNumPoint) return 0.;
double dblBasisPairFitnessPenalty = 0.;
for (int i = 0; i < iNumPoint; ++i) {
double dblPredictorOrdinate = _sbfr.predictorOrdinate (i);
dblBasisPairFitnessPenalty += _sbfr.weight (i) * _lbe.shapedBasisFunctionResponse
(dblPredictorOrdinate, iBasisIndexI) * _lbe.shapedBasisFunctionResponse
(dblPredictorOrdinate, iBasisIndexR);
}
return dblBasisPairFitnessPenalty / iNumPoint;
}
/**
* Compute the Basis Pair Penalty Coefficient for the Best Fit and the Curvature Penalties
*
* @param iBasisIndexI I Basis Index (I is the Summation Index)
* @param iBasisIndexR R Basis Index (R is the Separator Index)
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*
* @return The Basis Pair Penalty Coefficient for the Fitness and the Curvature Penalties
*/
public double basisPairConstraintCoefficient (
final int iBasisIndexI,
final int iBasisIndexR)
throws java.lang.Exception
{
return basisPairCurvaturePenalty (iBasisIndexI, iBasisIndexR) + basisPairLengthPenalty (iBasisIndexI,
iBasisIndexR) + basisBestFitPenalty (iBasisIndexI, iBasisIndexR);
}
/**
* Compute the Penalty Constraint for the Basis Pair
*
* @param iBasisIndexR R Basis Index (R is the Separator Index)
*
* @return Penalty Constraint for the Basis Pair
*
* @throws java.lang.Exception Thrown if the Inputs are invalid
*/
public double basisPairPenaltyConstraint (
final int iBasisIndexR)
throws java.lang.Exception
{
if (null == _sbfr) return 0.;
int iNumPoint = _sbfr.numPoint();
if (0 == iNumPoint) return 0.;
double dblBasisPairPenaltyConstraint = 0.;
for (int i = 0; i < iNumPoint; ++i) {
double dblPredictorOrdinate = _sbfr.predictorOrdinate (i);
dblBasisPairPenaltyConstraint += _sbfr.weight (i) * _lbe.shapedBasisFunctionResponse
(dblPredictorOrdinate, iBasisIndexR) * _sbfr.response (i);
}
return dblBasisPairPenaltyConstraint / iNumPoint;
}
}