LowerSFixedSeries.java
package org.drip.specialfunction.incompletegamma;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* 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
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - 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>LowerSFixedSeries</i> implements Lower Incomplete Gamma Expansion Series. The References are:
*
* <br><br>
* <ul>
* <li>
* Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of
* Definite Integrals involving Elementary Functions via Differentiation of Special Functions
* <i>Applicable Algebra in Engineering, Communications, and </i> <b>1 (2)</b> 149-165
* </li>
* <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>
* Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over
* e<sup>iπx</sup> x<sup>(1/x)</sup> between 1 and ∞
* https://arxiv.org/pdf/0912.3844.pdf <b>arXiV</b>
* </li>
* <li>
* National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions
* https://dlmf.nist.gov/8
* </li>
* <li>
* Wikipedia (2019): Incomplete Gamma Function
* https://en.wikipedia.org/wiki/Incomplete_gamma_function
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</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 Implementation Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/gammaincomplete/README.md">Upper/Lower Incomplete Gamma Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class LowerSFixedSeries extends org.drip.numerical.estimation.R1ToR1Series
{
private double _s = java.lang.Double.NaN;
private double _logGammaS = java.lang.Double.NaN;
/**
* Construct the R<sup>1</sup> To R<sup>1</sup> Weierstrass Limit Series
*
* @param s Incomplete Gamma s
* @param termCount Count of the Number of Terms
*
* @return The R<sup>1</sup> To R<sup>1</sup> Weierstrass Limit Series
*/
public static final LowerSFixedSeries WeierstrassLimit (
final double s,
final int termCount)
{
java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
java.util.TreeMap<java.lang.Integer, java.lang.Double>();
for (int termIndex = 0; termIndex <= termCount; ++termIndex)
{
termWeightMap.put (
termIndex,
1.
);
}
try
{
return new LowerSFixedSeries (
org.drip.specialfunction.incompletegamma.LowerSFixedSeriesTerm.WeierstrassLimit (s),
termWeightMap,
s,
0 == s ? 1. : new org.drip.specialfunction.loggamma.NemesAnalyticEstimator (null).evaluate (s)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the R<sup>1</sup> To R<sup>1</sup> NIST (2019) Limit Series
*
* @param s Incomplete Gamma s
* @param termCount Count of the Number of Terms
*
* @return The R<sup>1</sup> To R<sup>1</sup> NIST (2019) Limit Series
*/
public static final LowerSFixedSeries NIST2019 (
final double s,
final int termCount)
{
try
{
double logGammaS = new org.drip.specialfunction.loggamma.NemesAnalyticEstimator (null).evaluate (s);
java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap = new
java.util.TreeMap<java.lang.Integer, java.lang.Double>();
for (int termIndex = 0; termIndex <= termCount; ++termIndex)
{
termWeightMap.put (
termIndex,
1.
);
}
return new LowerSFixedSeries (
org.drip.specialfunction.incompletegamma.LowerSFixedSeriesTerm.NIST2019 (
s,
logGammaS
),
termWeightMap,
s,
logGammaS
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* LowerSFixedSeries Constructor
*
* @param r1ToR1SeriesTerm R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
* @param termWeightMap Error Term Weight Map
* @param s s
* @param logGammaS Log (Gamma (s))
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public LowerSFixedSeries (
final org.drip.numerical.estimation.R1ToR1SeriesTerm r1ToR1SeriesTerm,
final java.util.TreeMap<java.lang.Integer, java.lang.Double> termWeightMap,
final double s,
final double logGammaS)
throws java.lang.Exception
{
super (
r1ToR1SeriesTerm,
false,
termWeightMap
);
if (!org.drip.numerical.common.NumberUtil.IsValid (_s = s) ||
!org.drip.numerical.common.NumberUtil.IsValid (_logGammaS = logGammaS))
{
throw new java.lang.Exception ("LowerSFixedSeries Constructor => Invalid Inputs");
}
}
/**
* Retrieve s
*
* @return s
*/
public double s()
{
return _s;
}
/**
* Retrieve Log (Gamma (s))
*
* @return Log (Gamma (s))
*/
public double logGammaS()
{
return _logGammaS;
}
}