R1ToR1SeriesTerm.java
package org.drip.numerical.estimation;
/*
* -*- 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>R1ToR1SeriesTerm</i> exposes the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term in the Ordered
* Series of the Numerical Estimate for a Function. 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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/estimation/README.md">Function Numerical Estimates/Corrections/Bounds</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class R1ToR1SeriesTerm
{
/**
* Construct the Asymptotic Series Expansion Term
*
* @return The Asymptotic Series Expansion Term
*/
public static final R1ToR1SeriesTerm Asymptotic()
{
return new R1ToR1SeriesTerm()
{
@Override public double value (
final int order,
final double x)
throws java.lang.Exception
{
if (0 >= order ||
!org.drip.numerical.common.NumberUtil.IsValid (x) || 0. == x)
{
throw new java.lang.Exception ("Asymptotic::R1ToR1SeriesTerm::value => Invalid Inputs");
}
return java.lang.Math.pow (
x,
-1. * order
);
}
};
}
/**
* Construct the Inverted Rising Exponential Series Expansion Term
*
* @return The Inverted Rising Exponential Series Expansion Term
*/
public static final R1ToR1SeriesTerm InvertedRisingExponential()
{
return new R1ToR1SeriesTerm()
{
@Override public double value (
final int order,
final double x)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception
("InvertedRisingExponential::R1ToR1SeriesTerm::evaluate => Invalid Inputs");
}
double risingExponential = 1.;
for (int orderIndex = 1; orderIndex <= order; ++orderIndex)
{
risingExponential = risingExponential * (x + orderIndex);
}
if (0. == risingExponential)
{
throw new java.lang.Exception
("InvertedRisingExponential::R1ToR1SeriesTerm::evaluate => Invalid Inputs");
}
return 1. / risingExponential;
}
};
}
/**
* Construct the Taylor Series Expansion Term
*
* @return The Taylor Series Expansion Term
*/
public static final R1ToR1SeriesTerm Taylor()
{
return new R1ToR1SeriesTerm()
{
@Override public double value (
final int order,
final double x)
throws java.lang.Exception
{
if (0 >= order ||
!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception ("Taylor::R1ToR1SeriesTerm::value => Invalid Inputs");
}
return java.lang.Math.pow (
x,
order
);
}
@Override public double derivative (
final int order,
final int derivativeOrder,
final double x)
throws java.lang.Exception
{
if (0 >= order ||
0 >= derivativeOrder ||
!org.drip.numerical.common.NumberUtil.IsValid (x))
{
throw new java.lang.Exception ("Taylor::R1ToR1SeriesTerm::derivative => Invalid Inputs");
}
return derivativeOrder > order ? 0. : org.drip.numerical.common.NumberUtil.NPK (
order,
derivativeOrder
) * java.lang.Math.pow (
x,
order - derivativeOrder
);
}
};
}
protected R1ToR1SeriesTerm()
{
}
/**
* Compute the Value of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
*
* @param order Order of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
* @param x X
*
* @return The Value of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public abstract double value (
final int order,
final double x)
throws java.lang.Exception;
/**
* Compute the Derivative of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
*
* @param order Order of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
* @param derivativeOrder Order of the R<sup>1</sup> To R<sup>1</sup> Series Derivative
* @param x X
*
* @return The Derivative of the R<sup>1</sup> To R<sup>1</sup> Series Expansion Term
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double derivative (
final int order,
final int derivativeOrder,
final double x)
throws java.lang.Exception
{
throw new java.lang.Exception ("R1ToR1SeriesTerm::value => Generic Derivative Not Implemented");
}
}