Package org.drip.function.e2erfc

Class ErrorFunctionComplement

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator

org.drip.function.e2erfc.ErrorFunctionComplement

public class ErrorFunctionComplement
extends R1ToR1IntegrandLimitEstimator

ErrorFunctionComplement implements the Error Function Complement (erfc). 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 erfc Estimation Function Implementation

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
ErrorFunctionComplement(R1ToR1Series r1ToR1SeriesGenerator, DerivativeControl dc)	ErrorFunctionComplement Constructor

Method Summary

Modifier and Type	Method	Description
static ErrorFunctionComplement	AsymptoticExpansion(int termCount)	Construct the Asymptotic Expansion Version of ErrorFunctionComplement
double	cdf(double x)	Compute the CDF Value for the given X
double	erf(double x)	Compute the erf Value for the given X
double	erfcx(double x)	Compute the erfcx Value for the given X
R1ToR1	integrand()	Retrieve the R1 To R1 erf Integrand
static ErrorFunctionComplement	InverseFactorialExpansion(int termCount)	Construct the Inverse Factorial Expansion Version of ErrorFunctionComplement
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

antiDerivative, conditionNumber, derivative, 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

ErrorFunctionComplement

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

ErrorFunctionComplement Constructor

Parameters:

r1ToR1SeriesGenerator - R¹ To R¹ Series Generator

dc - Differential Control

Throws:

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

Method Details

AsymptoticExpansion

public static final ErrorFunctionComplement AsymptoticExpansion(int termCount)

Construct the Asymptotic Expansion Version of ErrorFunctionComplement

Parameters:

termCount - Count of the Number of Terms

Returns:

The Asymptotic Expansion Version of ErrorFunctionComplement

InverseFactorialExpansion

public static final ErrorFunctionComplement InverseFactorialExpansion(int termCount)

Construct the Inverse Factorial Expansion Version of ErrorFunctionComplement

Parameters:

termCount - Count of the Number of Terms

Returns:

The Inverse Factorial Expansion Version of ErrorFunctionComplement

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

erf

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

Compute the erf Value for the given X

Parameters:

x - X

Returns:

The erf Value

Throws:

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

erfcx

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

Compute the erfcx Value for the given X

Parameters:

x - X

Returns:

The erfcx Value

Throws:

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