Package org.drip.function.e2erf

Class ErrorFunction

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator

org.drip.function.e2erf.ErrorFunction

Direct Known Subclasses:

AbramowitzStegun

public class ErrorFunction
extends R1ToR1IntegrandLimitEstimator

ErrorFunction implements the E₂ Error Function (erf). 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
ErrorFunction(R1ToR1Series r1ToR1SeriesGenerator, DerivativeControl dc)	ErrorFunction Constructor

Method Summary

Modifier and Type	Method	Description
R1ToR1	antiDerivative()	Compute the Anti-Derivative Function
double	cdf(double x)	Compute the CDF Value for the given X
double	derivative(double z, int order)	Calculate the derivative as a double
double	erfc(double x)	Compute the erfc Value for the given X
double	gaussianDensityIntegral(double a, double b, R1UnivariateNormal r1UnivariateNormal)	Compute the E2 erf Gaussian Density Integral over -inf to +inf
static ErrorFunction	HansHeinrichBurmannConvergent()	Construct the Convergent Hans Heinrich Burmann Version of the E2 erf
static ErrorFunction	HansHeinrichBurmannSchopfSupancic2014()	Construct the Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E2 erf
R1ToR1	integrand()	Retrieve the R1 To R1 erf Integrand
static ErrorFunction	MacLaurin(int termCount)	Construct the Euler-MacLaurin Instance of the E2 erf
double	q(double x)	Compute the Q Value for the given X
R1Estimate	seriesEstimateNative(double x)	Compute the Built-in Higher Order Series Estimates

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

ErrorFunction

public ErrorFunction(R1ToR1Series r1ToR1SeriesGenerator,
DerivativeControl dc)
              throws java.lang.Exception

ErrorFunction Constructor

Parameters:

r1ToR1SeriesGenerator - R¹ To R¹ Series Generator

dc - Differential Control

Throws:

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

Method Details

MacLaurin

public static final ErrorFunction MacLaurin(int termCount)

Construct the Euler-MacLaurin Instance of the E₂ erf

Parameters:

termCount - The Count of Approximation Terms

Returns:

The Euler-MacLaurin Instance of the E₂ erf

HansHeinrichBurmannConvergent

public static final ErrorFunction HansHeinrichBurmannConvergent()

Construct the Convergent Hans Heinrich Burmann Version of the E₂ erf

Returns:

The Convergent Hans Heinrich Burmann Version of the E₂ erf

HansHeinrichBurmannSchopfSupancic2014

public static final ErrorFunction HansHeinrichBurmannSchopfSupancic2014()

Construct the Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E₂ erf

Returns:

The Schopf-Supancic (2014) Hans Heinrich Burmann Version of the E₂ erf

derivative

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

Description copied from class: R1ToR1

Calculate the derivative as a double

Overrides:

derivative in class R1ToR1

Parameters:

z - 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

antiDerivative

public R1ToR1 antiDerivative()

Description copied from class: R1ToR1

Compute the Anti-Derivative Function

Overrides:

antiDerivative in class R1ToR1

Returns:

The Anti-Derivative Function

seriesEstimateNative

public R1Estimate seriesEstimateNative(double x)

Description copied from class: R1ToR1Estimator

Compute the Built-in Higher Order Series Estimates

Overrides:

seriesEstimateNative in class R1ToR1Estimator

Parameters:

x - X

Returns:

The Built-in Higher Order Series Estimates

integrand

public R1ToR1 integrand()

Description copied from class: R1ToR1IntegrandLimitEstimator

Retrieve the R¹ To R¹ erf Integrand

Specified by:

integrand in class R1ToR1IntegrandLimitEstimator

Returns:

The R¹ To R¹ erf Integrand

q

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

Compute the Q Value for the given X

Parameters:

x - X

Returns:

The Q Value

Throws:

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

cdf

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

Compute the CDF Value for the given X

Parameters:

x - X

Returns:

The CDF Value

Throws:

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

erfc

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

Compute the erfc Value for the given X

Parameters:

x - X

Returns:

The erfc Value

Throws:

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

gaussianDensityIntegral

public double gaussianDensityIntegral(double a,
double b,
R1UnivariateNormal r1UnivariateNormal)
                               throws java.lang.Exception

Compute the E₂ erf Gaussian Density Integral over -inf to +inf

Parameters:

a - The Scale Parameter

b - The Displacement Parameter

r1UnivariateNormal - The R¹ Gaussian Distribution Parameters

Returns:

The E₂ erf Gaussian Density Integral over -inf to +inf

Throws:

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