LowerEulerIntegral.java

package org.drip.specialfunction.incompletegamma;

/*
 * -*- 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>LowerEulerIntegral</i> implements the Euler's Second Kind Integral Version of the Lower Incomplete
 * Gamma Function. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
 *              Definite Integrals involving Elementary Functions via Differentiation of Special Functions
 *              <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
 *      </li>
 *      <li>
 *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
 *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
 *      </li>
 *      <li>
 *          Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
 *              e<sup>iÏ€x</sup> x<sup>(1/x)</sup> between 1 and ∞
 *              https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
 *      </li>
 *      <li>
 *          National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions
 *              https://dlmf.nist.gov/8
 *      </li>
 *      <li>
 *          Wikipedia (2019): Incomplete Gamma Function
 *              https://en.wikipedia.org/wiki/Incomplete_gamma_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/gammaincomplete/README.md">Upper/Lower Incomplete Gamma Functions</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

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

    /**
     * LowerEulerIntegral Constructor
     * 
     * @param limit The Upper Limit
     * @param dc The Derivative Control
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public LowerEulerIntegral (
        final org.drip.numerical.differentiation.DerivativeControl dc,
        final double limit)
        throws java.lang.Exception
    {
        super (dc);

        if (!org.drip.numerical.common.NumberUtil.IsValid (_limit = limit))
        {
            throw new java.lang.Exception ("LowerEulerIntegral Constructor => Invalid Inputs");
        }
    }

    /**
     * Retrieve the Upper Limit
     * 
     * @return The Upper Limit
     */

    public double limit()
    {
        return _limit;
    }

    @Override public double evaluate (
        final double s)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (s))
        {
            throw new java.lang.Exception ("LowerEulerIntegral::evaluate => Invalid Inputs");
        }

        return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
            0.,
            _limit,
            10000
        ).integrate (
            new org.drip.function.definition.R1ToR1 (null)
            {
                @Override public double evaluate (
                    final double t)
                    throws java.lang.Exception
                {
                    return java.lang.Double.isInfinite (t) ? 0. : (0 == t ? 1. :
                        java.lang.Math.pow (
                            t,
                            s - 1
                        )
                    ) * java.lang.Math.exp (-t);
                }
            }
        );
    }
}