LeftHatShapeControl.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>LeftHatShapeControl</i> implements the BasisHatShapeControl interface for the left hat basis set as
 * 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 LeftHatShapeControl extends org.drip.spline.bspline.BasisHatShapeControl {

    /**
     * LeftHatShapeControl constructor
     * 
     * @param dblLeftPredictorOrdinate The Left Predictor Ordinate
     * @param dblRightPredictorOrdinate The Right Predictor Ordinate
     * @param strShapeControlType Type of the Shape Controller to be used - NONE, LINEAR/QUADRATIC Rational
     * @param dblTension Tension of the Tension Hat Function
     * 
     * @throws java.lang.Exception Thrown if the input is invalid
     */

    public LeftHatShapeControl (
        final double dblLeftPredictorOrdinate,
        final double dblRightPredictorOrdinate,
        final java.lang.String strShapeControlType,
        final double dblTension)
        throws java.lang.Exception
    {
        super (dblLeftPredictorOrdinate, dblRightPredictorOrdinate, strShapeControlType, dblTension);
    }

    @Override public double evaluate (
        final double dblPredictorOrdinate)
        throws java.lang.Exception
    {
        if (!in (dblPredictorOrdinate)) return 0.;

        double dblWidth = right() - left();

        double dblScale = 1. / (dblWidth * (6. + 6. * tension() * dblWidth + 2. * tension() * dblWidth *
            dblWidth));

        if (SHAPE_CONTROL_RATIONAL_LINEAR.equalsIgnoreCase (shapeControlType()))
            return dblScale / (1. + tension() * (right() - dblPredictorOrdinate));

        if (SHAPE_CONTROL_RATIONAL_QUADRATIC.equalsIgnoreCase (shapeControlType()))
            return dblScale / (1. + tension() * (right() - dblPredictorOrdinate) * (dblPredictorOrdinate -
                left()) / dblWidth);

        return (java.lang.Math.exp (-tension() * (right() - dblPredictorOrdinate))) / (dblWidth * (6. + 6. *
            tension() * dblWidth + tension() * dblWidth * dblWidth));
    }

    @Override public double derivative (
        final double dblPredictorOrdinate,
        final int iOrder)
        throws java.lang.Exception
    {
        if (0 >= iOrder) throw new java.lang.Exception ("LeftHatShapeControl::derivative => Invalid Inputs");

        if (!in (dblPredictorOrdinate) || 0. == tension()) return 0.;

        double dblWidth = right() - left();

        double dblScale = 1. / (dblWidth * (6. + 6. * tension() * dblWidth + 2. * tension() * dblWidth *
            dblWidth));

        if (SHAPE_CONTROL_RATIONAL_LINEAR.equalsIgnoreCase (shapeControlType()))
            return dblScale * org.drip.numerical.common.NumberUtil.Factorial (iOrder) * java.lang.Math.pow
                (tension(), iOrder) * java.lang.Math.pow (1. + tension() * (right() - dblPredictorOrdinate),
                    -iOrder - 1);

        if (SHAPE_CONTROL_RATIONAL_EXPONENTIAL.equalsIgnoreCase (shapeControlType()))
            return (java.lang.Math.pow (tension(), iOrder) * java.lang.Math.exp (-tension() * (right() -
                dblPredictorOrdinate))) / (dblWidth * (6. + 6. * tension() * dblWidth + tension() * dblWidth
                    * dblWidth));

        return super.derivative (dblPredictorOrdinate, iOrder);
    }

    @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 ("LeftHatShapeControl::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;

        double dblWidth = right() - left();

        if (SHAPE_CONTROL_RATIONAL_LINEAR.equalsIgnoreCase (shapeControlType()))
            return (java.lang.Math.log ((1. + tension() * (right() - dblBoundedBegin)) / (1. + tension() *
                (right() - dblBoundedEnd)))) / tension() / (dblWidth * (6. + 6. * tension() * dblWidth + 2. *
                    tension() * dblWidth * dblWidth));

        if (SHAPE_CONTROL_RATIONAL_EXPONENTIAL.equalsIgnoreCase (shapeControlType()))
            return (java.lang.Math.exp (tension() * (dblBoundedEnd - right())) - java.lang.Math.exp
                (tension() * (dblBoundedBegin - right()))) / tension() / (dblWidth * (6. + 6. * tension() *
                    dblWidth + tension() * dblWidth * dblWidth));

        return super.integrate (dblBoundedBegin, dblBoundedEnd);
    }

    @Override public double normalizer()
        throws java.lang.Exception
    {
        double dblWidth = right() - left();

        if (0. == tension()) return dblWidth;

        if (SHAPE_CONTROL_RATIONAL_LINEAR.equalsIgnoreCase (shapeControlType()))
            return (java.lang.Math.log ((1. + tension() * dblWidth))) / tension() / (dblWidth * (6. + 6. *
                tension() * dblWidth + 2. * tension() * dblWidth * dblWidth));

        if (SHAPE_CONTROL_RATIONAL_EXPONENTIAL.equalsIgnoreCase (shapeControlType()))
            return (1. - java.lang.Math.exp (tension() * dblWidth)) / tension() / (dblWidth * (6. + 6. *
                tension() * dblWidth + tension() * dblWidth * dblWidth));

        return super.integrate (left(), right());
    }
}