Package org.drip.numerical.estimation

Class R1ToR1Estimator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

Direct Known Subclasses:

CumulativeSeriesEstimator, E0ErrorFunction, E1ErrorFunction, ErrorFunctionComplementInverse, ErrorFunctionInverse, Estimator, GeneralizedErrorFunction, InfiniteSumEstimator, LowerSFixed, NemesAnalytic, NemesAnalyticEstimator, R1ToR1IntegrandEstimator, R1ToR1IntegrandLimitEstimator, RaabeSeriesEstimator, RamanujanSeries, RamanujanSeriesEstimator, SeriesEstimator, StirlingSeries, StirlingSeriesEstimator, UpperSFixed, WindschitlTothAnalytic, WindschitlTothAnalyticEstimator

public abstract class R1ToR1Estimator
extends R1ToR1

R1ToR1Estimator exposes the Stubs behind R¹ - R¹ Approximate Numerical Estimators. The References are:

• Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function Computers and Mathematics with Applications 61 (11) 3364-3369
• National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.11
• Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n! https://arxiv.org/abs/1003.2907 arXiv
• Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
• Wikipedia (2019): Stirling's Approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Function Numerical Estimates/Corrections/Bounds

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1ToR1Estimator(DerivativeControl dc)	R1 - R1 Estimator Constructor

Method Summary

Modifier and Type	Method	Description
R1Estimate	boundedEstimate(double x)	Estimate a Bounded Numerical Approximation of the Function Value
R1Estimate	seriesEstimate(double x, java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap, R1ToR1Series r1ToR1SeriesGenerator)	Compute the Higher Order Series Estimates
R1Estimate	seriesEstimateNative(double x)	Compute the Built-in Higher Order Series Estimates

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, conditionNumber, derivative, differential, differential, evaluate, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

R1ToR1Estimator

public R1ToR1Estimator(DerivativeControl dc)

R¹ - R¹ Estimator Constructor

Parameters:

dc - The Derivative Control

Method Details

boundedEstimate

public R1Estimate boundedEstimate(double x)

Estimate a Bounded Numerical Approximation of the Function Value

Parameters:

x - X

Returns:

The Bounded Numerical Approximation

seriesEstimate

public R1Estimate seriesEstimate(double x,
java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap,
R1ToR1Series r1ToR1SeriesGenerator)

Compute the Higher Order Series Estimates

Parameters:

x - X

termWeightMap - Error Term Weight Map

r1ToR1SeriesGenerator - R¹ To R¹ Series Generator

Returns:

The Higher Order Series Estimates

seriesEstimateNative

public R1Estimate seriesEstimateNative(double x)

Compute the Built-in Higher Order Series Estimates

Parameters:

x - X

Returns:

The Built-in Higher Order Series Estimates