UpperLimitPowerEstimate.java
- package org.drip.sample.gammaincomplete;
- import org.drip.numerical.common.FormatUtil;
- import org.drip.numerical.integration.NewtonCotesQuadratureGenerator;
- import org.drip.service.env.EnvManager;
- import org.drip.specialfunction.incompletegamma.UpperLimitPowerIntegrand;
- /*
- * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
- */
- /*!
- * Copyright (C) 2019 Lakshmi Krishnamurthy
- *
- * This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
- * calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
- * FX, and structured products.
- *
- * https://lakshmidrip.github.io/DROP/
- *
- * DROP is composed of three main modules:
- *
- * - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
- * - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
- * - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
- *
- * DROP Analytics Core implements libraries for the following:
- * - Fixed Income Analytics
- * - Asset Backed Analytics
- * - XVA Analytics
- * - Exposure and Margin Analytics
- *
- * DROP Portfolio Core implements libraries for the following:
- * - Asset Allocation Analytics
- * - Transaction Cost Analytics
- *
- * DROP Numerical Core implements libraries for the following:
- * - Statistical Learning Library
- * - Numerical Optimizer Library
- * - Machine Learning Library
- * - Spline Builder Library
- *
- * 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
- * - 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>UpperLimitPowerEstimate</i> illustrates the Estimation of the Integral of the Product of the Limit
- * Raised to an Exponent and the corresponding Upper 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>iπx</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 (2019a): 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/NumericalCore.md">Numerical Core Module</a></li>
- * <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
- * <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
- * <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gammaincomplete/README.md">Estimates of Incomplete Gamma Functions</a></li>
- * </ul>
- *
- * @author Lakshmi Krishnamurthy
- */
- public class UpperLimitPowerEstimate
- {
- private static final void QuadratureComparison (
- final UpperLimitPowerIntegrand upperLimitPowerIntegrand,
- final double s,
- final double limitExponent,
- final double[] leftArray,
- final double[] rightArray,
- final int intermediatePointCount)
- throws Exception
- {
- System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
- System.out.println ("\t| QUADRATURE COMPARISON - s => " + FormatUtil.FormatDouble (s, 1, 1, 1.) + " | Exponent => " + FormatUtil.FormatDouble (limitExponent, 1, 1, 1.));
- System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
- System.out.println ("\t| L -> R: ||");
- System.out.println ("\t| - s ||");
- System.out.println ("\t| - [Comparison Pair] ||");
- System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
- for (double left : leftArray)
- {
- String display = "\t|" + FormatUtil.FormatDouble (left, 1, 1, 1.) + " => ";
- for (double right : rightArray)
- {
- display = display + "[" + FormatUtil.FormatDouble (
- NewtonCotesQuadratureGenerator.Zero_PlusOne (
- left,
- right,
- intermediatePointCount
- ).integrate (upperLimitPowerIntegrand), 4, 2, 1.
- ) + " - " + FormatUtil.FormatDouble (
- upperLimitPowerIntegrand.integrate (
- left,
- right
- ), 4, 2, 1.
- ) + "] |";
- }
- System.out.println (display + "|");
- }
- System.out.println ("\t|--------------------------------------------------------------------------------------------------------------------------||");
- }
- public static final void main (
- final String[] argumentArray)
- throws Exception
- {
- EnvManager.InitEnv ("");
- int intermediatePointCount = 100;
- double[] leftArray =
- {
- 1.,
- 2.,
- 3.,
- 4.,
- 5.,
- };
- double[] rightArray =
- {
- 10.,
- 15.,
- 20.,
- 25.,
- 30.,
- };
- double[] sArray =
- {
- 3.,
- 4.,
- 5.,
- 6.,
- 7.,
- };
- double[] limitExponentArray =
- {
- 3.,
- 4.,
- 5.,
- 6.,
- 7.,
- };
- for (double s : sArray)
- {
- for (double limitExponent : limitExponentArray)
- {
- UpperLimitPowerIntegrand upperLimitPowerIntegrand = new UpperLimitPowerIntegrand (
- null,
- s,
- limitExponent
- );
- QuadratureComparison (
- upperLimitPowerIntegrand,
- s,
- limitExponent,
- leftArray,
- rightArray,
- intermediatePointCount
- );
- }
- }
- EnvManager.TerminateEnv();
- }
- }