EnERFMacLaurin.java

  1. package org.drip.sample.erf;

  3. import org.drip.function.enerf.GeneralizedErrorFunction;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  15.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  16.  *      FX, and structured products.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three main modules:
  21.  *  
  22.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  25.  * 
  26.  *  DROP Analytics Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Asset Backed Analytics
  29.  *  - XVA Analytics
  30.  *  - Exposure and Margin Analytics
  31.  * 
  32.  *  DROP Portfolio Core implements libraries for the following:
  33.  *  - Asset Allocation Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Numerical Core implements libraries for the following:
  37.  *  - Statistical Learning Library
  38.  *  - Numerical Optimizer Library
  39.  *  - Machine Learning Library
  40.  *  - Spline Builder Library
  41.  * 
  42.  *  Documentation for DROP is Spread Over:
  43.  * 
  44.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  45.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  46.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  47.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  48.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  49.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  50.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  51.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  52.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  53.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  54.  * 
  55.  *  Licensed under the Apache License, Version 2.0 (the "License");
  56.  *      you may not use this file except in compliance with the License.
  57.  *   
  58.  *  You may obtain a copy of the License at
  59.  *      http://www.apache.org/licenses/LICENSE-2.0
  60.  *  
  61.  *  Unless required by applicable law or agreed to in writing, software
  62.  *      distributed under the License is distributed on an "AS IS" BASIS,
  63.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  64.  *  
  65.  *  See the License for the specific language governing permissions and
  66.  *      limitations under the License.
  67.  */

  69. /**
  70.  * <i>EnERFMacLaurin</i> illustrates the MacLaurin Series Based Estimates for E<sub>n</sub> erf. The
  71.  * References are:
  72.  * 
  73.  * <br><br>
  74.  *  <ul>
  75.  *      <li>
  76.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  77.  *              on Mathematics</b>
  78.  *      </li>
  79.  *      <li>
  80.  *          Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error
  81.  *              Function <i>IEEE Transactions on Communications</i> <b>59 (11)</b> 2939-2944
  82.  *      </li>
  83.  *      <li>
  84.  *          Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function
  85.  *              Routines and Test Drivers <i>ACM Transactions on Mathematical Software</i> <b>19 (1)</b>
  86.  *              22-32
  87.  *      </li>
  88.  *      <li>
  89.  *          Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of
  90.  *              Linear and Non-linear Heat Transfer and Diffusion
  91.  *              https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
  92.  *      </li>
  93.  *      <li>
  94.  *          Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function
  95.  *      </li>
  96.  *  </ul>
  97.  *
  98.  *  <br><br>
  99.  *  <ul>
  100.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  101.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  102.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/README.md">Function</a></li>
  103.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/feed/erf/README.md">E<sup>2</sup> and E<sup>n</sup> erf Estimation</a></li>
  104.  *  </ul>
  105.  *
  106.  * @author Lakshmi Krishnamurthy
  107.  */

  109. public class EnERFMacLaurin
  110. {

  112.     public static final void main (
  113.         final String[] argumentArray)
  114.         throws Exception
  115.     {
  116.         EnvManager.InitEnv ("");

  118.         double[] xArray =
  119.         {
  120.             -3.25,
  121.             -3.00,
  122.             -2.75,
  123.             -2.50,
  124.             -2.25,
  125.             -2.00,
  126.             -1.75,
  127.             -1.50,
  128.             -1.25,
  129.             -1.00,
  130.             -0.75,
  131.             -0.50,
  132.             -0.25,
  133.              0.00,
  134.              0.25,
  135.              0.50,
  136.              0.75,
  137.              1.00,
  138.              1.25,
  139.              1.50,
  140.              1.75,
  141.              2.00,
  142.              2.25,
  143.              2.50,
  144.              2.75,
  145.              3.00,
  146.              3.25
  147.         };
  148.         int[] degreeArray = 
  149.         {
  150.             0,
  151.             1,
  152.             2,
  153.             3,
  154.             4,
  155.             5
  156.         };
  157.         int termCount = 50;

  159.         GeneralizedErrorFunction[] erfnArray = new GeneralizedErrorFunction[degreeArray.length];

  161.         for (int degree : degreeArray)
  162.         {
  163.             erfnArray[degree] = GeneralizedErrorFunction.MacLaurin (
  164.                 degree,
  165.                 termCount
  166.             );
  167.         }

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

  171.         System.out.println ("\t|                                                                  E_n MacLaurin erf Estimate                                                                     ||");

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

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

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

  179.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 0)                                                                                                                ||");

  181.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 1)                                                                                                                ||");

  183.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 2)                                                                                                                ||");

  185.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 3)                                                                                                                ||");

  187.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 4)                                                                                                                ||");

  189.         System.out.println ("\t|                - MacLaurin Estimate (Degree = 5)                                                                                                                ||");

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

  193.         for (double x : xArray)
  194.         {
  195.             System.out.println (
  196.                 "\t| " + FormatUtil.FormatDouble (x, 1, 2, 1.) + " => " +
  197.                 FormatUtil.FormatDouble (erfnArray[0].evaluate (x), 1, 2, 1.) + " | " +
  198.                 FormatUtil.FormatDouble (erfnArray[1].evaluate (x), 2, 2, 1.) + " | " +
  199.                 FormatUtil.FormatDouble (erfnArray[2].evaluate (x), 1, 2, 1.) + " | " +
  200.                 FormatUtil.FormatDouble (erfnArray[3].evaluate (x), 14, 0, 1.) + " | " +
  201.                 FormatUtil.FormatDouble (erfnArray[4].evaluate (x), 38, 0, 1.) + " | " +
  202.                 FormatUtil.FormatDouble (erfnArray[5].evaluate (x), 64, 0, 1.) + " ||"
  203.             );
  204.         }

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

  208.         EnvManager.TerminateEnv();
  209.     }
  210. }
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