fr.cnes.sirius.patrius.math.special

Class Erf

java.lang.Object

fr.cnes.sirius.patrius.math.special.Erf

public final class Erf
extends Object

This is a utility class that provides computation methods related to the error functions.

Version:

$Id: Erf.java 18108 2017-10-04 06:45:27Z bignon $

Method Summary

Modifier and Type	Method and Description
static double	erf(double x) Returns the error function.
static double	erf(double x1, double x2) Returns the difference between erf(x1) and erf(x2).
static double	erfc(double x) Returns the complementary error function.
static double	erfcInv(double x) Returns the inverse erfc.
static double	erfInv(double x) Returns the inverse erf.

Methods inherited from class java.lang.Object

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

Method Detail

erf

public static double erf(double x)

Returns the error function.

erf(x) = 2/√π ₀∫^x e^-t2dt

This implementation computes erf(x) using the regularized gamma function, following Erf, equation (3)

The value returned is always between -1 and 1 (inclusive). If abs(x) > 40, then erf(x) is indistinguishable from either 1 or -1 as a double, so the appropriate extreme value is returned.

Parameters:

x - the value.

Returns:

the error function erf(x)

Throws:

MaxCountExceededException - if the algorithm fails to converge.

See Also:

Gamma.regularizedGammaP(double, double, double, int)

erfInv

public static double erfInv(double x)

Returns the inverse erf.

This implementation is described in the paper: Approximating the erfinv function by Mike Giles, Oxford-Man Institute of Quantitative Finance, which was published in GPU Computing Gems, volume 2, 2010. The source code is available here.

Parameters:

x - the value

Returns:

t such that x = erf(t)

Since:

4.5

erfc

public static double erfc(double x)

Returns the complementary error function.

erfc(x) = 2/√π _x∫^∞ e^-t2dt
= 1 - erf(x)

This implementation computes erfc(x) using the regularized gamma function, following Erf, equation (3).

The value returned is always between 0 and 2 (inclusive). If abs(x) > 40, then erf(x) is indistinguishable from either 0 or 2 as a double, so the appropriate extreme value is returned.

Parameters:

x - the value

Returns:

the complementary error function erfc(x)

Throws:

MaxCountExceededException - if the algorithm fails to converge.

Since:

2.2

See Also:

Gamma.regularizedGammaQ(double, double, double, int)

erf

public static double erf(double x1,
                         double x2)

Returns the difference between erf(x1) and erf(x2). The implementation uses either erf(double) or erfc(double) depending on which provides the most precise result.

Parameters:

x1 - the first value

x2 - the second value

Returns:

erf(x2) - erf(x1)

erfcInv

public static double erfcInv(double x)

Returns the inverse erfc.

Parameters:

x - the value

Returns:

t such that x = erfc(t)

Since:

4.5