GaussIntegralEstimate.java
- package org.drip.sample.digamma;
- import org.drip.numerical.common.FormatUtil;
- import org.drip.numerical.estimation.R1ToR1IntegrandEstimator;
- import org.drip.service.env.EnvManager;
- import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
- import org.drip.specialfunction.digamma.IntegralEstimator;
- /*
- * -*- 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>GaussIntegralEstimate</i> demonstrates the Estimation of the Digamma Function using the Gauss Integral.
- * The References are:
- *
- * <br><br>
- * <ul>
- * <li>
- * Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions <b>Dover Book on
- * Mathematics</b>
- * </li>
- * <li>
- * Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the
- * Zeta-Functions https://arxiv.org/abs/1606.02044 <b>arXiv</b>
- * </li>
- * <li>
- * Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function
- * Analogue <i>Integral Transforms and Special Functions</i> <b>28 (28)</b> 846-858
- * </li>
- * <li>
- * Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
- * University Press</b> New York
- * </li>
- * <li>
- * Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_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/sample/README.md">DROP API Construction and Usage</a></li>
- * <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/digamma/README.md">Estimates of the Digamma Function</a></li>
- * </ul>
- *
- * @author Lakshmi Krishnamurthy
- */
- public class GaussIntegralEstimate
- {
- public static final void main (
- final String[] argumentArray)
- throws Exception
- {
- EnvManager.InitEnv ("");
- int termCount = 1000000;
- double[] zArray =
- {
- 0.5,
- 1.0,
- 1.5,
- 2.0,
- 2.5,
- 3.0,
- 3.5,
- 4.0,
- 4.5,
- 5.0,
- 5.5,
- 6.0,
- 6.5,
- 7.0,
- 7.5,
- 8.0,
- 8.5,
- 9.0,
- 9.5,
- };
- R1ToR1IntegrandEstimator gaussIntegral = IntegralEstimator.Gauss();
- CumulativeSeriesEstimator abramowitzStegun2007 =
- CumulativeSeriesEstimator.AbramowitzStegun2007 (termCount);
- System.out.println ("\t|--------------------------------------||");
- System.out.println ("\t| GAUSS INTEGRAL DIGAMMA ESTIMATE ||");
- System.out.println ("\t|--------------------------------------||");
- System.out.println ("\t| L -> R: ||");
- System.out.println ("\t| - z ||");
- System.out.println ("\t| - Abramowitz-Stegun (2007) ||");
- System.out.println ("\t| - Gaussian Integral ||");
- System.out.println ("\t|--------------------------------------||");
- for (double z : zArray)
- {
- System.out.println (
- "\t|" + FormatUtil.FormatDouble (z, 1, 1, 1.) + " => " +
- FormatUtil.FormatDouble (
- abramowitzStegun2007.evaluate (z),
- 1, 10, 1.
- ) + " | " + FormatUtil.FormatDouble (
- gaussIntegral.evaluate (z),
- 1, 10, 1.
- ) + " ||"
- );
- }
- System.out.println ("\t|--------------------------------------||");
- EnvManager.TerminateEnv();
- }
- }