LowerRegularized.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>LowerRegularized</i> implements the Regularized Version of the Lower Incomplete Gamma. 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 abstract class LowerRegularized
{
/**
* Construct the Gauss Continued Version of Lower Regularized Incomplete Gamma Function
*
* @param n Count of the Number of Terms
*
* @return Gauss Continued Version of Lower Regularized Incomplete Gamma Function
*/
public static final LowerRegularized GaussContinuedFraction (
final int n)
{
return new LowerRegularized()
{
@Override public double p (
final double s,
final double z)
throws java.lang.Exception
{
double p = org.drip.specialfunction.incompletegamma.GaussContinuedFraction.Lower (
z,
s,
n
) / new org.drip.specialfunction.gamma.NemesAnalytic (null).evaluate (s);
return p > 1. ? 1. : p;
}
};
}
/**
* Construct the Euler Integral Version of Lower Regularized Incomplete Gamma Function
*
* @return Euler Integral Version of Lower Regularized Incomplete Gamma Function
*/
public static final LowerRegularized EulerIntegral()
{
return new LowerRegularized()
{
@Override public double p (
final double s,
final double z)
throws java.lang.Exception
{
double p = new org.drip.specialfunction.incompletegamma.LowerEulerIntegral (
null,
z
).evaluate (s) / new org.drip.specialfunction.gamma.NemesAnalytic (null).evaluate (s);
return p > 1. ? 1. : p;
}
};
}
/**
* Construct the Weierstrass Limit Version of Lower Regularized Incomplete Gamma Function
*
* @param n Count of the Number of Terms
*
* @return Weierstrass Limit Version of Lower Regularized Incomplete Gamma Function
*/
public static final LowerRegularized WeierstrassLimit (
final int n)
{
return new LowerRegularized()
{
@Override public double p (
final double s,
final double z)
throws java.lang.Exception
{
double p = org.drip.specialfunction.incompletegamma.LowerSFixed.WeierstrassLimit (
s,
n
).evaluate (z) / new org.drip.specialfunction.gamma.NemesAnalytic (null).evaluate (s);
return p > 1. ? 1. : p;
}
};
}
/**
* Construct the NIST (2019) Version of Lower Regularized Incomplete Gamma Function
*
* @param n Count of the Number of Terms
*
* @return NIST (2019) Version of Lower Regularized Incomplete Gamma Function
*/
public static final LowerRegularized NIST2019 (
final int n)
{
return new LowerRegularized()
{
@Override public double p (
final double s,
final double z)
throws java.lang.Exception
{
double p = org.drip.specialfunction.incompletegamma.LowerSFixed.NIST2019 (
s,
n
).evaluate (z) / new org.drip.specialfunction.gamma.NemesAnalytic (null).evaluate (s);
return p > 1. ? 1. : p;
}
};
}
private LowerRegularized()
{
}
/**
* Compute p (s, z)
*
* @param s s
* @param z z
*
* @return p(s, z)
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public abstract double p (
final double s,
final double z)
throws java.lang.Exception;
}