ASeriesSequence.java
package org.drip.sample.lanczos;
import java.util.Map;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.lanczos.ASeriesGenerator;
/*
* -*- 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>ASeriesSequence</i> illustrates the Generation of the Lanczos A Series for different Values of the g
* Control. The References are:
*
* <br><br>
* <ul>
* <li>
* Godfrey, P. (2001): Lanczos Implementation of the Gamma Function
* http://www.numericana.com/answer/info/godfrey.htm
* </li>
* <li>
* Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): <i>Numerical Recipes:
* The Art of Scientific Computing 3rd Edition</i> <b>Cambridge University Press</b> New York
* </li>
* <li>
* Pugh, G. R. (2004): <i>An Analysis of the Lanczos Gamma Approximation</i> Ph. D. <b>University of
* British Columbia</b>
* </li>
* <li>
* Toth V. T. (2016): Programmable Calculators – The Gamma Function
* http://www.rskey.org/CMS/index.php/the-library/11
* </li>
* <li>
* Wikipedia (2019): Lanczos Approximation https://en.wikipedia.org/wiki/Lanczos_approximation
* </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/sample/README.md">Sample</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/lanczos/README.md">Lanczos Gamma Calculation Scheme Illustration</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ASeriesSequence
{
private static final void DisplaySeries (
final int g,
final Map<Integer, Double> orderedSeries)
throws Exception
{
String series = "\t|" + FormatUtil.FormatDouble (g, 2, 0, 1.) + " => ";
for (Map.Entry<Integer, Double> seriesEntry : orderedSeries.entrySet())
{
series = series + " " + FormatUtil.FormatDouble (seriesEntry.getValue(), 6, 0, 1.) + " |";
}
System.out.println (series + "|");
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double z = 1.;
int termCount = 10;
int[] gArray =
{
3,
4,
5,
6,
7,
8,
9,
10
};
System.out.println
("\t|---------------------------------------------------------------------------------------------------------------------||");
System.out.println
("\t| A-SERIES SEQUENCE ||");
System.out.println
("\t|---------------------------------------------------------------------------------------------------------------------||");
System.out.println
("\t| L -> R: ||");
System.out.println
("\t| - g ||");
System.out.println
("\t| - A Series Coefficients ||");
System.out.println
("\t|---------------------------------------------------------------------------------------------------------------------||");
for (int g : gArray)
{
DisplaySeries (
g,
ASeriesGenerator.Standard (
g,
termCount
).generate (
0.,
z
)
);
}
System.out.println
("\t|---------------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}