org.apache.commons.math3.special
Class Erf

java.lang.Object
  org.apache.commons.math3.special.Erf

public class Erf
extends Object

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

Version:

$Id: Erf.java 1456905 2013-03-15 11:37:35Z luc $

Field Summary

private static double

X_CRIT The number X_CRIT is used by erf(double, double) internally.

Constructor Summary

private

Erf() Default constructor.

Method Summary

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

Field Detail

X_CRIT

private static final double X_CRIT

The number X_CRIT is used by erf(double, double) internally. This number solves erf(x)=0.5 within 1ulp. More precisely, the current implementations of erf(double) and erfc(double) satisfy:
erf(X_CRIT) < 0.5,
erf(Math.nextUp(X_CRIT) > 0.5,
erfc(X_CRIT) = 0.5, and
erfc(Math.nextUp(X_CRIT) < 0.5

See Also:

Constant Field Values

Constructor Detail

Erf

private Erf()

Default constructor. Prohibit instantiation.

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)

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)

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:

3.2

erfcInv

public static double erfcInv(double x)

Returns the inverse erfc.

Parameters:

x - the value

Returns:

t such that x = erfc(t)

Since:

3.2