Package org.drip.numerical.estimation

Class R0ToR1Series

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.RkToR1Series

org.drip.numerical.estimation.R0ToR1Series

Direct Known Subclasses:

PSeriesGenerator

public class R0ToR1Series
extends RkToR1Series

R0ToR1Series generates a Series of Weighted Numerical R⁰ To R¹ Terms. 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
R0ToR1Series(R0ToR1SeriesTerm r0Tor1SeriesTerm, boolean proportional, java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap, boolean cumulative)	R0ToR1Series Constructor

Method Summary

Modifier and Type	Method	Description
boolean	cumulative()	Indicate if the Series Term is Incremental or Cumulative
double	derivative(double x, int order)	Calculate the derivative as a double
double	evaluate(double x)	Evaluate for the given variate
java.util.TreeMap<java.lang.Integer,java.lang.Double>	generate(double zeroOrder)	Generate the Series Expansion using the R0 To R1 Term
R0ToR1SeriesTerm	r0Tor1SeriesTerm()	Retrieve the R0 To R1 Series Term

Methods inherited from class org.drip.numerical.estimation.RkToR1Series

proportional, termWeightMap

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

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

Methods inherited from class java.lang.Object

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

Constructor Details

R0ToR1Series

public R0ToR1Series(R0ToR1SeriesTerm r0Tor1SeriesTerm,
boolean proportional,
java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap,
boolean cumulative)
             throws java.lang.Exception

R0ToR1Series Constructor

Parameters:

r0Tor1SeriesTerm - R⁰ To R¹ Series Term

proportional - TRUE - The Series Term is Proportional

termWeightMap - Error Term Weight Map

cumulative - TRUE - The Series Term is Cumulative

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

r0Tor1SeriesTerm

public R0ToR1SeriesTerm r0Tor1SeriesTerm()

Retrieve the R⁰ To R¹ Series Term

Returns:

The R⁰ To R¹ Series Term

cumulative

public boolean cumulative()

Indicate if the Series Term is Incremental or Cumulative

Returns:

TRUE - The Series Term is Cumulative

generate

public java.util.TreeMap<java.lang.Integer,java.lang.Double> generate(double zeroOrder)

Generate the Series Expansion using the R⁰ To R¹ Term

Parameters:

zeroOrder - The Zero Order Estimate

Returns:

The Series Expansion

evaluate

public double evaluate(double x)
                throws java.lang.Exception

Description copied from class: R1ToR1

Evaluate for the given variate

Specified by:

evaluate in class R1ToR1

Parameters:

x - Variate

Returns:

Returns the calculated value

Throws:

java.lang.Exception - Thrown if evaluation cannot be done

derivative

public double derivative(double x,
int order)
                  throws java.lang.Exception

Description copied from class: R1ToR1

Calculate the derivative as a double

Overrides:

derivative in class R1ToR1

Parameters:

x - Variate at which the derivative is to be calculated

order - Order of the derivative to be computed

Returns:

The Derivative

Throws:

java.lang.Exception - Thrown if Inputs are Invalid