Package org.drip.function.e2erf

Class AbramowitzStegun

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator

org.drip.function.e2erf.ErrorFunction

org.drip.function.e2erf.AbramowitzStegun

public abstract class AbramowitzStegun
extends ErrorFunction

AbramowitzStegun implements the E₂ (erf) Estimator using Abramowitz-Stegun Scheme. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error Function IEEE Transactions on Communications 59 (11) 2939-2944
• Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function Routines and Test Drivers ACM Transactions on Mathematical Software 19 (1) 22-32
• Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of Linear and Non-linear Heat Transfer and Diffusion https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
• Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d To R^d Function Analysis
• Package = E₂ erf and erf^-1 Implementations

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
AbramowitzStegun(AbramowitzStegunSeriesGenerator abramowitzStegunSeriesGenerator, DerivativeControl dc, double maximumError)	E2AbramowitzStegun Constructor

Method Summary

Modifier and Type	Method	Description
static AbramowitzStegun	InversePolynomial4()	Construct the Inverse Degree 4 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
static AbramowitzStegun	InversePolynomial6()	Construct the Inverse Degree 6 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
double	maximumError()	Retrieve the Maximum Error
static AbramowitzStegun	MixedPolynomial3()	Construct the Mixed Degree 3 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
static AbramowitzStegun	MixedPolynomial5()	Construct the Mixed Degree 5 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
static AbramowitzStegun	NumericalRecipe2007()	Construct the Numerical Recipe Version of Abramowitz-Stegun E2 erf Estimator

Methods inherited from class org.drip.function.e2erf.ErrorFunction

antiDerivative, cdf, derivative, erfc, gaussianDensityIntegral, HansHeinrichBurmannConvergent, HansHeinrichBurmannSchopfSupancic2014, integrand, MacLaurin, q, seriesEstimateNative

Methods inherited from class org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator

evaluate, leftLimit

Methods inherited from class org.drip.numerical.estimation.R1ToR1Estimator

boundedEstimate, seriesEstimate

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

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

AbramowitzStegun

public AbramowitzStegun(AbramowitzStegunSeriesGenerator abramowitzStegunSeriesGenerator,
DerivativeControl dc,
double maximumError)
                 throws java.lang.Exception

E2AbramowitzStegun Constructor

Parameters:

abramowitzStegunSeriesGenerator - Abramowitz Stegun Series Generator

dc - The Derivative Control

maximumError - Maximum Error

Throws:

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

Method Details

InversePolynomial4

public static final AbramowitzStegun InversePolynomial4()

Construct the Inverse Degree 4 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

Returns:

The Inverse Degree 4 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

MixedPolynomial3

public static final AbramowitzStegun MixedPolynomial3()

Construct the Mixed Degree 3 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

Returns:

The Mixed Degree 3 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

InversePolynomial6

public static final AbramowitzStegun InversePolynomial6()

Construct the Inverse Degree 6 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

Returns:

The Inverse Degree 6 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

MixedPolynomial5

public static final AbramowitzStegun MixedPolynomial5()

Construct the Mixed Degree 5 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

Returns:

The Mixed Degree 5 Polynomial Version of Abramowitz-Stegun E₂ erf Estimator

NumericalRecipe2007

public static final AbramowitzStegun NumericalRecipe2007()

Construct the Numerical Recipe Version of Abramowitz-Stegun E₂ erf Estimator

Returns:

The Numerical Recipe Version of Abramowitz-Stegun E₂ erf Estimator

maximumError

public double maximumError()

Retrieve the Maximum Error

Returns:

The Maximum Error