KohlrauschMomentEstimate2.java

  1. package org.drip.sample.scaledexponential;

  3. import org.drip.function.definition.R1ToR1;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.specialfunction.definition.ScaledExponentialEstimator;
  7. import org.drip.specialfunction.gamma.NemesAnalytic;
  8. import org.drip.specialfunction.scaledexponential.RelaxationTimeDistributionSeriesEstimator;

  10. /*
  11.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  12.  */

  14. /*!
  15.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  18.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  19.  *      FX, and structured products.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three main modules:
  24.  *  
  25.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  28.  * 
  29.  *  DROP Analytics Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Asset Backed Analytics
  32.  *  - XVA Analytics
  33.  *  - Exposure and Margin Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Transaction Cost Analytics
  38.  * 
  39.  *  DROP Numerical Core implements libraries for the following:
  40.  *  - Statistical Learning Library
  41.  *  - Numerical Optimizer Library
  42.  *  - Machine Learning Library
  43.  *  - Spline Builder Library
  44.  * 
  45.  *  Documentation for DROP is Spread Over:
  46.  * 
  47.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  48.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  49.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  50.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  51.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  52.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  53.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  54.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  55.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  56.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  57.  * 
  58.  *  Licensed under the Apache License, Version 2.0 (the "License");
  59.  *      you may not use this file except in compliance with the License.
  60.  *   
  61.  *  You may obtain a copy of the License at
  62.  *      http://www.apache.org/licenses/LICENSE-2.0
  63.  *  
  64.  *  Unless required by applicable law or agreed to in writing, software
  65.  *      distributed under the License is distributed on an "AS IS" BASIS,
  66.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  67.  *  
  68.  *  See the License for the specific language governing permissions and
  69.  *      limitations under the License.
  70.  */

  72. /**
  73.  * <i>KohlrauschMomentEstimate2</i> illustrates the Estimation of the Moments of the Kohlrausch Function
  74.  * using the Relaxation Time Distribution. The References are:
  75.  * 
  76.  * <br><br>
  77.  *  <ul>
  78.  *      <li>
  79.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  80.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  81.  *      </li>
  82.  *      <li>
  83.  *          Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye
  84.  *              Susceptibilities in Glassy Systems <i>Physical Review E</i> <b>65 (6)</b> 061510
  85.  *      </li>
  86.  *      <li>
  87.  *          Wikipedia (2019): Stretched Exponential Function
  88.  *              https://en.wikipedia.org/wiki/Stretched_exponential_function
  89.  *      </li>
  90.  *      <li>
  91.  *          Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic
  92.  *              Error-Bounds, Double Exponential Transform, and Open Source Implementation <i>libkw</i>
  93.  *              <i>Algorithm</i> <b>5 (4)</b> 604-628
  94.  *      </li>
  95.  *      <li>
  96.  *          Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions <i>Journal of Chemical
  97.  *              Physics</i> <b>116 (8)</b> 3204-3209
  98.  *      </li>
  99.  *  </ul>
  100.  *
  101.  *  <br><br>
  102.  *  <ul>
  103.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  104.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  105.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Project</a></li>
  106.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/ode/README.md">Special Function Ordinary Differential Equations</a></li>
  107.  *  </ul>
  108.  *
  109.  * @author Lakshmi Krishnamurthy
  110.  */

  112. public class KohlrauschMomentEstimate2
  113. {

  115.     public static final void main (
  116.         final String[] argumentArray)
  117.         throws Exception
  118.     {
  119.         EnvManager.InitEnv ("");

  121.         int termCount = 160;
  122.         double[] betaArray =
  123.         {
  124.              0.1,
  125.              0.2,
  126.              0.3,
  127.              0.4,
  128.              0.5,
  129.              0.6,
  130.              0.7,
  131.              0.8,
  132.              0.9,
  133.         };
  134.         int[] momentArray =
  135.         {
  136.             1,
  137.             2,
  138.             3,
  139.         };

  141.         R1ToR1 gammaEstimator = new NemesAnalytic (null);

  143.         for (double beta : betaArray)
  144.         {
  145.             ScaledExponentialEstimator scaledExponentialEstimator = new ScaledExponentialEstimator (
  146.                 beta,
  147.                 1.
  148.             );

  150.             RelaxationTimeDistributionSeriesEstimator relaxationTimeDistributionSeriesEstimator =
  151.                 RelaxationTimeDistributionSeriesEstimator.Standard (
  152.                     beta,
  153.                     gammaEstimator,
  154.                     termCount
  155.                 );

  157.             String display = "\t| [" + FormatUtil.FormatDouble (beta, 1, 1, 1., false) + "] =>";

  159.             for (int moment : momentArray)
  160.             {
  161.                 display = display + " {" + FormatUtil.FormatDouble (
  162.                     scaledExponentialEstimator.higherMoment (
  163.                         moment,
  164.                         gammaEstimator
  165.                     ), 1, 3, 1., false
  166.                 ) + " - " + FormatUtil.FormatDouble (
  167.                     scaledExponentialEstimator.higherMomentUsingDensity (
  168.                         moment,
  169.                         relaxationTimeDistributionSeriesEstimator,
  170.                         gammaEstimator
  171.                     ), 1, 3, 1., false
  172.                 ) + "} |";
  173.             }

  175.             System.out.println (display + "|");
  176.         }

  178.         EnvManager.TerminateEnv();
  179.     }
  180. }
Created with JaCoCo 0.7.9.201702052155