EulerIntegrandNEstimate.java

  1. package org.drip.sample.beta;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.beta.IntegrandEstimator;
  6. import org.drip.specialfunction.beta.LogGammaEstimator;

  8. /*
  9.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  10.  */

  12. /*!
  13.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  17.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  18.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  19.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  20.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  21.  *      and computational support.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three modules:
  26.  *  
  27.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  30.  * 
  31.  *  DROP Product Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Loan Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Asset Liability Management Analytics
  39.  *  - Capital Estimation Analytics
  40.  *  - Exposure Analytics
  41.  *  - Margin Analytics
  42.  *  - XVA Analytics
  43.  * 
  44.  *  DROP Computational Core implements libraries for the following:
  45.  *  - Algorithm Support
  46.  *  - Computation Support
  47.  *  - Function Analysis
  48.  *  - Model Validation
  49.  *  - Numerical Analysis
  50.  *  - Numerical Optimizer
  51.  *  - Spline Builder
  52.  *  - Statistical Learning
  53.  * 
  54.  *  Documentation for DROP is Spread Over:
  55.  * 
  56.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  57.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  58.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  59.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  60.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  61.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  62.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  63.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  64.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  65.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  66.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  67.  * 
  68.  *  Licensed under the Apache License, Version 2.0 (the "License");
  69.  *      you may not use this file except in compliance with the License.
  70.  *   
  71.  *  You may obtain a copy of the License at
  72.  *      http://www.apache.org/licenses/LICENSE-2.0
  73.  *  
  74.  *  Unless required by applicable law or agreed to in writing, software
  75.  *      distributed under the License is distributed on an "AS IS" BASIS,
  76.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  77.  *  
  78.  *  See the License for the specific language governing permissions and
  79.  *      limitations under the License.
  80.  */

  82. /**
  83.  * <i>EulerIntegrandNEstimate</i> illustrates the Beta Function Estimation using the Euler Integrand "N"
  84.  * Scheme. The References are:
  85.  * 
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  90.  *              on Mathematics</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  94.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  95.  *      </li>
  96.  *      <li>
  97.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  98.  *              University Press</b> New York
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
  102.  *      </li>
  103.  *      <li>
  104.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  105.  *      </li>
  106.  *  </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  112.  *      <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>
  113.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/beta/README.md">Estimates of the Beta Functions</a></li>
  114.  *  </ul>
  115.  *
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class EulerIntegrandNEstimate
  120. {

  122.     public static final void main (
  123.         final String[] argumentArray)
  124.         throws Exception
  125.     {
  126.         EnvManager.InitEnv ("");

  128.         int eulerIntegrandTermCount = 10000;
  129.         int logGammaTermCount = 1000000;
  130.         double[] xArray =
  131.         {
  132.             1.,
  133.             2.,
  134.             3.,
  135.             4.,
  136.             5.,
  137.             6.,
  138.         };
  139.         double[] yArray =
  140.         {
  141.             1.,
  142.             2.,
  143.             3.,
  144.             4.,
  145.             5.,
  146.             6.,
  147.         };

  149.         IntegrandEstimator eulerFirstIntegrandEstimator0p5 = IntegrandEstimator.EulerFirstN (
  150.             eulerIntegrandTermCount,
  151.             0.5
  152.         );

  154.         IntegrandEstimator eulerFirstIntegrandEstimator2p0 = IntegrandEstimator.EulerFirstN (
  155.             eulerIntegrandTermCount,
  156.             2.0
  157.         );

  159.         LogGammaEstimator logGammaEstimator = LogGammaEstimator.Weierstrass (logGammaTermCount);

  161.         System.out.println ("\t|-----------------------------------------------------------||");

  163.         System.out.println ("\t|                 BETA FUNCTION ESTIMATION                  ||");

  165.         System.out.println ("\t|-----------------------------------------------------------||");

  167.         System.out.println ("\t|        L -> R:                                            ||");

  169.         System.out.println ("\t|                - x                                        ||");

  171.         System.out.println ("\t|                - y                                        ||");

  173.         System.out.println ("\t|                - Gamma Based Estimate                     ||");

  175.         System.out.println ("\t|                - Euler Integral First Kind Estimate       ||");

  177.         System.out.println ("\t|                - Trigonometric Integral Estimate          ||");

  179.         System.out.println ("\t|-----------------------------------------------------------||");

  181.         for (double x : xArray)
  182.         {
  183.             for (double y : yArray)
  184.             {
  185.                 System.out.println (
  186.                     "\t| [" +
  187.                     FormatUtil.FormatDouble (x, 1, 1, 1.) + "," +
  188.                     FormatUtil.FormatDouble (y, 1, 1, 1.) + "] =>" +
  189.                     FormatUtil.FormatDouble (
  190.                         Math.exp (
  191.                             logGammaEstimator.evaluate (
  192.                                 x,
  193.                                 y
  194.                             )
  195.                         ), 1, 10, 1.
  196.                     ) + " |" +
  197.                     FormatUtil.FormatDouble (
  198.                         eulerFirstIntegrandEstimator0p5.evaluate (
  199.                             x,
  200.                             y
  201.                         ), 1, 10, 1.
  202.                     ) + " |" +
  203.                     FormatUtil.FormatDouble (
  204.                         eulerFirstIntegrandEstimator2p0.evaluate (
  205.                             x,
  206.                             y
  207.                         ), 1, 10, 1.
  208.                     ) + " ||"
  209.                 );
  210.             }
  211.         }

  213.         System.out.println ("\t|-----------------------------------------------------------||");

  215.         EnvManager.TerminateEnv();
  216.     }
  217. }
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