NumericalEstimate.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;
  7. import org.drip.specialfunction.beta.SummationSeriesEstimator;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */

  13. /*!
  14.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  18.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  19.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  20.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  21.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  22.  *      and computational support.
  23.  *  
  24.  *      https://lakshmidrip.github.io/DROP/
  25.  *  
  26.  *  DROP is composed of three modules:
  27.  *  
  28.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  29.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  30.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  31.  * 
  32.  *  DROP Product Core implements libraries for the following:
  33.  *  - Fixed Income Analytics
  34.  *  - Loan Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Asset Liability Management Analytics
  40.  *  - Capital Estimation Analytics
  41.  *  - Exposure Analytics
  42.  *  - Margin Analytics
  43.  *  - XVA Analytics
  44.  * 
  45.  *  DROP Computational Core implements libraries for the following:
  46.  *  - Algorithm Support
  47.  *  - Computation Support
  48.  *  - Function Analysis
  49.  *  - Model Validation
  50.  *  - Numerical Analysis
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Statistical Learning
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>NumericalEstimate</i> illustrates the Beta Function Estimation using Integrand Schemes. The References
  85.  * are:
  86.  * 
  87.  * <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  91.  *              on Mathematics</b>
  92.  *      </li>
  93.  *      <li>
  94.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  95.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  96.  *      </li>
  97.  *      <li>
  98.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  99.  *              University Press</b> New York
  100.  *      </li>
  101.  *      <li>
  102.  *          Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
  103.  *      </li>
  104.  *      <li>
  105.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  113.  *      <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>
  114.  *      <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>
  115.  *  </ul>
  116.  *
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class NumericalEstimate
  121. {

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

  129.         int eulerIntegrandRightHalfPlaneTermCount = 1000;
  130.         int trigonometricIntegrandTermCount = 1000;
  131.         int eulerIntegrandTermCount = 1000;
  132.         int summationTermCount = 1000000;
  133.         int logGammaTermCount = 1000000;
  134.         double[] xArray =
  135.         {
  136.             1.,
  137.             2.,
  138.             3.,
  139.             4.,
  140.             5.,
  141.             6.,
  142.         };
  143.         double[] yArray =
  144.         {
  145.             1.,
  146.             2.,
  147.             3.,
  148.             4.,
  149.             5.,
  150.             6.,
  151.         };

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

  155.         IntegrandEstimator eulerFirstIntegrandEstimator = IntegrandEstimator.EulerFirst
  156.             (eulerIntegrandTermCount);

  158.         IntegrandEstimator eulerFirstRightHalfPlane = IntegrandEstimator.EulerFirstRightPlane
  159.             (eulerIntegrandRightHalfPlaneTermCount);

  161.         IntegrandEstimator trigonometricIntegrandEstimator = IntegrandEstimator.Trigonometric
  162.             (trigonometricIntegrandTermCount);

  164.         SummationSeriesEstimator summationSeriesEstimator = SummationSeriesEstimator.AbramowitzStegun2007
  165.             (summationTermCount);

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

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

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

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

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

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

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

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

  183.         System.out.println ("\t|                - Euler Integral First Right Half Plane Estimate                         ||");

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

  187.         System.out.println ("\t|                - Summation Series Estimate                                              ||");

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

  191.         for (double x : xArray)
  192.         {
  193.             for (double y : yArray)
  194.             {
  195.                 System.out.println (
  196.                     "\t| [" +
  197.                     FormatUtil.FormatDouble (x, 1, 1, 1.) + "," +
  198.                     FormatUtil.FormatDouble (y, 1, 1, 1.) + "] =>" +
  199.                     FormatUtil.FormatDouble (
  200.                         Math.exp (
  201.                             logGammaEstimator.evaluate (
  202.                                 x,
  203.                                 y
  204.                             )
  205.                         ), 1, 10, 1.
  206.                     ) + " |" +
  207.                     FormatUtil.FormatDouble (
  208.                         eulerFirstIntegrandEstimator.evaluate (
  209.                             x,
  210.                             y
  211.                         ), 1, 10, 1.
  212.                     ) + " |" +
  213.                     FormatUtil.FormatDouble (
  214.                         eulerFirstRightHalfPlane.evaluate (
  215.                             x,
  216.                             y
  217.                         ), 1, 10, 1.
  218.                     ) + " |" +
  219.                     FormatUtil.FormatDouble (
  220.                         trigonometricIntegrandEstimator.evaluate (
  221.                             x,
  222.                             y
  223.                         ), 1, 10, 1.
  224.                     ) + " |" +
  225.                     FormatUtil.FormatDouble (
  226.                         summationSeriesEstimator.evaluate (
  227.                             x,
  228.                             y
  229.                         ), 1, 10, 1.
  230.                     ) + " ||"
  231.                 );
  232.             }
  233.         }

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

  237.         EnvManager.TerminateEnv();
  238.     }
  239. }
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