RamanujanSeries.java
package org.drip.specialfunction.gamma;
/*
* -*- 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>RamanujanSeries</i> implements the Ramanujan Series Version of the Gamma Function Approximation. The
* References are:
*
* <br><br>
* <ul>
* <li>
* Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function <i>Computers and
* Mathematics with Applications</i> <b>61 (11)</b> 3364-3369
* </li>
* <li>
* National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical
* Functions https://dlmf.nist.gov/5.11
* </li>
* <li>
* Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n!
* https://arxiv.org/abs/1003.2907 <b>arXiv</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): Stirling's Approximation
* https://en.wikipedia.org/wiki/Stirling%27s_approximation
* </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/gamma/README.md">Analytic/Series/Integral Gamma Estimators</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class RamanujanSeries extends org.drip.numerical.estimation.R1ToR1Estimator
{
/**
* RamanujanSeries Constructor
*
* @param dc The Derivative Control
*/
public RamanujanSeries (
final org.drip.numerical.differentiation.DerivativeControl dc)
{
super (dc);
}
@Override public double evaluate (
final double z)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (z) || 0. > z)
{
throw new java.lang.Exception ("RamanujanSeries::evaluate => Invalid Inputs");
}
double x = z - 1.;
return java.lang.Math.sqrt (java.lang.Math.PI) * java.lang.Math.pow (
x / java.lang.Math.E,
x
) * java.lang.Math.pow (
8. * x * x * x + 4. * x * x + x + (1./ 30.),
1. / 6.
);
}
@Override public org.drip.numerical.estimation.R1Estimate boundedEstimate (
final double x)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x) || 0. > x)
{
return null;
}
double exponentialComponent = java.lang.Math.sqrt (java.lang.Math.PI) * java.lang.Math.pow (
x / java.lang.Math.E,
x
);
double upperBound = exponentialComponent * java.lang.Math.pow (
8. * x * x * x + 4. * x * x + x + (1./ 30.),
1. / 6.
);
try
{
return new org.drip.numerical.estimation.R1Estimate (
upperBound,
exponentialComponent * java.lang.Math.pow (
8. * x * x * x + 4. * x * x + x + (1./ 100.),
1. / 6.
),
upperBound
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}