ModifiedBesselFirstKindEstimator.java

package org.drip.specialfunction.definition;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 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>ModifiedBesselFirstKindEstimator</i> exposes the Estimator for the Modified Bessel Function of the
 * First Kind. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
 *              on Mathematics</b>
 *      </li>
 *      <li>
 *          Arfken, G. B., and H. J. Weber (2005): <i>Mathematical Methods for Physicists 6<sup>th</sup>
 *              Edition</i> <b>Harcourt</b> San Diego
 *      </li>
 *      <li>
 *          Temme N. M. (1996): <i>Special Functions: An Introduction to the Classical Functions of
 *              Mathematical Physics 2<sup>nd</sup> Edition</i> <b>Wiley</b> New York
 *      </li>
 *      <li>
 *          Watson, G. N. (1995): <i>A Treatise on the Theory of Bessel Functions</i> <b>Cambridge University
 *              Press</b>
 *      </li>
 *      <li>
 *          Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function
 *      </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/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/definition/README.md">Definition of Special Function Estimators</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public abstract class ModifiedBesselFirstKindEstimator implements org.drip.function.definition.R2ToR1
{

    /**
     * Construct the Alpha Positive Asymptotic Version of ModifiedBesselFirstKindEstimator
     * 
     * @param gammaEstimator Gamma Estimator
     * 
     * @return Alpha Positive Asymptotic Version of ModifiedBesselFirstKindEstimator
     */

    public static final ModifiedBesselFirstKindEstimator AlphaPositiveAsymptote (
        final org.drip.function.definition.R1ToR1 gammaEstimator)
    {
        return null == gammaEstimator ? null : new ModifiedBesselFirstKindEstimator()
        {
            @Override public double bigI (
                final double alpha,
                final double z)
                throws java.lang.Exception
            {
                if (0. > alpha ||
                    !org.drip.numerical.common.NumberUtil.IsValid (z))
                {
                    throw new java.lang.Exception
                        ("ModifiedBesselFirstKindEstimator::AlphaPositiveAsymptote => Invalid Inputs");
                }

                return java.lang.Math.pow (
                    0.5 * z,
                    alpha
                ) / gammaEstimator.evaluate (alpha + 1.);
            }
        };
    }

    /**
     * Evaluate Modified Bessel Function First Kind I given Alpha and z
     * 
     * @param alpha Alpha
     * @param z Z
     *  
     * @return Modified Bessel Function First Kind I Value
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public abstract double bigI (
        final double alpha,
        final double z)
        throws java.lang.Exception;

    @Override public double evaluate (
        final double alpha,
        final double z)
        throws java.lang.Exception
    {
        return bigI (
            alpha,
            z
        );
    }
}