QuadraticRationalShapeControl.java

package org.drip.function.r1tor1;

/*
 * -*- 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>QuadraticRationalShapeControl</i> implements the deterministic rational shape control functionality on
 * top of the estimator basis splines inside - [0,...,1) - Globally [x_0,...,x_1):
 * <br><br>
 *          y = 1 / [1 + lambda * x * (1-x)]
 * <br><br>
 *      where is the normalized ordinate mapped as
 * <br><br>
 *          x ==== (x - x_i-1) / (x_i - x_i-1)
 *
 *  <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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/r1tor1/README.md">Built-in R<sup>1</sup> To R<sup>1</sup> Functions</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class QuadraticRationalShapeControl extends org.drip.function.definition.R1ToR1 {
    private double _dblLambda = java.lang.Double.NaN;

    /**
     * QuadraticRationalShapeControl constructor
     * 
     * @param dblLambda Tension Parameter
     * 
     * @throws java.lang.Exception Thrown if the inputs are invalid
     */

    public QuadraticRationalShapeControl (
        final double dblLambda)
        throws java.lang.Exception
    {
        super (null);

        if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLambda = dblLambda))
            throw new java.lang.Exception ("QuadraticRationalShapeControl ctr: Invalid tension");
    }

    @Override public double evaluate (
        final double dblX)
        throws java.lang.Exception
    {
        return 1. / (1. + _dblLambda * dblX * (1. - dblX));
    }

    @Override public double derivative (
        final double dblX,
        final int iOrder)
        throws java.lang.Exception
    {
        if (0. == _dblLambda) return 0.;

        double dblD2BetaDX2 = -2. * _dblLambda;
        double dblDBetaDX = _dblLambda * (1. - 2. * dblX);
        double dblBeta = 1. + _dblLambda * dblX * (1. - dblX);

        if (1 == iOrder) return -1. * dblDBetaDX / (dblBeta * dblBeta);

        if (2 == iOrder)
            return (2. * dblDBetaDX * dblDBetaDX - dblBeta * dblD2BetaDX2) / (dblBeta * dblBeta * dblBeta);

        return super.derivative (dblX, 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 ("QuadraticRationalShapeControl::integrate => Invalid Inputs");

        double dblAlpha = java.lang.Math.sqrt (0.25 * (_dblLambda + 4.) / _dblLambda);

        return -0.5 * (java.lang.Math.log ((dblEnd - dblAlpha - 0.5) * (dblBegin + dblAlpha - 0.5) /
            (dblEnd + dblAlpha - 0.5) / (dblBegin - dblAlpha - 0.5))) / dblAlpha / _dblLambda;
    }

    /**
     * Retrieve the shape control coefficient
     * 
     * @return Shape control coefficient
     */

    public double getShapeControlCoefficient()
    {
        return _dblLambda;
    }

    public static final void main (
        final java.lang.String[] astrArgs)
        throws java.lang.Exception
    {
        QuadraticRationalShapeControl qrsc = new QuadraticRationalShapeControl (1.);

        System.out.println (qrsc.derivative (0., 2));

        System.out.println (qrsc.derivative (1., 2));
    }
}