ExponentialTensionLeftRaw.java
package org.drip.spline.bspline;
/*
* -*- 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>ExponentialTensionLeftRaw</i> implements the TensionBasisHat interface in accordance with the raw left
* exponential hat basis function laid out in the basic framework outlined in Koch and Lyche (1989), Koch and
* Lyche (1993), and Kvasov (2000) Papers.
*
* <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/bspline/README.md">de Boor Rational/Exponential/Tension B-Splines</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class ExponentialTensionLeftRaw extends org.drip.spline.bspline.TensionBasisHat {
/**
* ExponentialTensionLeftRaw constructor
*
* @param dblLeftPredictorOrdinate The Left Predictor Ordinate
* @param dblRightPredictorOrdinate The Right Predictor Ordinate
* @param dblTension Tension of the Tension Hat Function
*
* @throws java.lang.Exception Thrown if the input is invalid
*/
public ExponentialTensionLeftRaw (
final double dblLeftPredictorOrdinate,
final double dblRightPredictorOrdinate,
final double dblTension)
throws java.lang.Exception
{
super (dblLeftPredictorOrdinate, dblRightPredictorOrdinate, dblTension);
}
@Override public double evaluate (
final double dblPredictorOrdinate)
throws java.lang.Exception
{
if (!in (dblPredictorOrdinate)) return 0.;
double dblAdjPredictorOrdinate = tension() * (dblPredictorOrdinate - left());
return (java.lang.Math.sinh (dblAdjPredictorOrdinate) - dblAdjPredictorOrdinate) / (tension() *
tension() * java.lang.Math.sinh (tension() * (right() - left())));
}
@Override public double derivative (
final double dblPredictorOrdinate,
final int iOrder)
throws java.lang.Exception
{
if (0 > iOrder)
throw new java.lang.Exception ("ExponentialTensionLeftRaw::derivative => Invalid Inputs");
if (!in (dblPredictorOrdinate)) return 0.;
double dblWidth = right() - left();
if (1 == iOrder)
return (java.lang.Math.cosh (tension() * (dblPredictorOrdinate - left())) - 1.) / (tension() *
java.lang.Math.sinh (tension() * dblWidth));
return java.lang.Math.pow (tension(), iOrder - 2) * (0 == iOrder % 2 ? java.lang.Math.sinh (tension()
* (dblPredictorOrdinate - left())) : java.lang.Math.cosh (tension() * (dblPredictorOrdinate -
left()))) / java.lang.Math.sinh (tension() * dblWidth);
}
@Override public double integrate (
final double dblBegin,
final double dblEnd)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblBegin) || !org.drip.numerical.common.NumberUtil.IsValid
(dblEnd))
throw new java.lang.Exception ("ExponentialTensionLeftRaw::integrate => Invalid Inputs");
double dblBoundedBegin = org.drip.numerical.common.NumberUtil.Bound (dblBegin, left(), right());
double dblBoundedEnd = org.drip.numerical.common.NumberUtil.Bound (dblEnd, left(), right());
if (dblBoundedBegin >= dblBoundedEnd) return 0.;
if (0. == tension()) return dblBoundedEnd - dblBoundedBegin;
return (java.lang.Math.cosh (dblBoundedEnd - left()) - java.lang.Math.cosh (dblBoundedBegin -
left()) - 0.5 * tension() * tension() * (((dblBoundedEnd - left()) * (dblBoundedEnd - left())) -
((dblBoundedBegin - left()) * (dblBoundedBegin - left())))) / (tension() * tension() *
tension() * java.lang.Math.sinh (tension() * (right() - left())));
}
@Override public double normalizer()
throws java.lang.Exception
{
double dblWidth = right() - left();
return (java.lang.Math.cosh (dblWidth) - 1. - 0.5 * tension() * tension() * dblWidth * dblWidth) /
(tension() * tension() * tension() * java.lang.Math.sinh (tension() * dblWidth));
}
}