Apache Commons Math 3.6.1 · org.apache.commons.math3.special.Erf

Modifier and Type	Field and Description
private static final double	X_CRIT The number `X_CRIT` is used by `erf(double, double)` internally.

Access	Constructor and Description
private	Erf() Default constructor.

Method Summary

Modifier and Type	Method and Description
public static double	Returns: the error function erf(x) erf(double the value. x) Returns the error function.
public static double	Returns: erf(x2) - erf(x1) erf(double the first value x1, double the second value x2) Returns the difference between erf(x1) and erf(x2).
public static double	Returns: the complementary error function erfc(x) erfc(double the value x) Returns the complementary error function.
public static double	Returns: t such that x = erfc(t) erfcInv(final double the value x) Returns the inverse erfc.
public static double	Returns: t such that x = erf(t) erfInv(final double the value x) Returns the inverse erf.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

X_CRIT	back to summary
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`

Constructor Detail

Erf	back to summary
private Erf() Default constructor. Prohibit instantiation.

Method Detail

erf back to summary

erf	back to summary
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:double the value. Returns:double the error function erf(x) Exceptions MaxCountExceededException: if the algorithm fails to converge. See Also `Gamma#regularizedGammaP(double, double, double, int)`

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:double: the value.

Returns:double

the error function erf(x)

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

erf	back to summary
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:double the first value x2:double the second value Returns:double erf(x2) - erf(x1)

erf

back to summary

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:double: the first value
x2:double: the second value

Returns:double

erf(x2) - erf(x1)

erfc back to summary

erfc	back to summary
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:double the value Returns:double the complementary error function erfc(x) Exceptions MaxCountExceededException: if the algorithm fails to converge. Since 2.2 See Also `Gamma#regularizedGammaQ(double, double, double, int)`

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:double: the value

Returns:double

the complementary error function erfc(x)

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

Since

2.2

erfcInv	back to summary
public static double erfcInv(final double x) Returns the inverse erfc. Parameters x:double the value Returns:double t such that x = erfc(t) Since 3.2

erfcInv

back to summary

public static double erfcInv(final double x)

Returns the inverse erfc.

Parameters

x:double: the value

Returns:double

t such that x = erfc(t)

Since

3.2

erfInv	back to summary
public static double erfInv(final 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:double the value Returns:double t such that x = erf(t) Since 3.2

erfInv

back to summary

public static double erfInv(final 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:double: the value

Returns:double

t such that x = erf(t)

Since

3.2

public Class Erf

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