KohlrauschFunctionEstimate2.java
package org.drip.sample.scaledexponential;
import org.drip.function.definition.R1ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.definition.ScaledExponentialEstimator;
import org.drip.specialfunction.gamma.NemesAnalytic;
import org.drip.specialfunction.scaledexponential.RelaxationTimeDistributionSeriesEstimator;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
* calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
* FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three main modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* 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
* - 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>KohlrauschFunctionEstimate2</i> illustrates the Construction and Usage of the Kohlrausch Function using
* the Relaxation Time Distribution. The References are:
*
* <br><br>
* <ul>
* <li>
* Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
* <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
* </li>
* <li>
* Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye
* Susceptibilities in Glassy Systems <i>Physical Review E</i> <b>65 (6)</b> 061510
* </li>
* <li>
* Wikipedia (2019): Stretched Exponential Function
* https://en.wikipedia.org/wiki/Stretched_exponential_function
* </li>
* <li>
* Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic
* Error-Bounds, Double Exponential Transform, and Open Source Implementation <i>libkw</i>
* <i>Algorithm</i> <b>5 (4)</b> 604-628
* </li>
* <li>
* Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions <i>Journal of Chemical
* Physics</i> <b>116 (8)</b> 3204-3209
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class KohlrauschFunctionEstimate2
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int termCount = 156;
double[] tArray =
{
0.1,
0.2,
0.3,
0.4,
0.5,
1.0,
2.0,
5.0,
10.0,
};
double[] betaArray =
{
0.1,
0.2,
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
};
R1ToR1 gammaEstimator = new NemesAnalytic (null);
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| SCALED EXPONENTIAL FUNCTION ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Beta ||");
System.out.println ("\t| - Values for different t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
for (double beta : betaArray)
{
ScaledExponentialEstimator scaledExponentialEstimator = new ScaledExponentialEstimator (
beta,
1.
);
RelaxationTimeDistributionSeriesEstimator relaxationTimeDistributionSeriesEstimator =
RelaxationTimeDistributionSeriesEstimator.Standard (
beta,
gammaEstimator,
termCount
);
String display = "\t| [" + FormatUtil.FormatDouble (beta, 1, 1, 1., false) + "] => ";
for (double t : tArray)
{
display = display + " {" + FormatUtil.FormatDouble (
scaledExponentialEstimator.evaluate (t), 1, 3, 1., false
) + " - " + FormatUtil.FormatDouble (
scaledExponentialEstimator.evaluateUsingDensity (
t,
relaxationTimeDistributionSeriesEstimator
), 1, 3, 1., false
) + "} |";
}
System.out.println (display + "|");
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}