Class Erf
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final double
The numberX_CRIT
is used byerf(double, double)
internally. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic 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.
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Field Details
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X_CRIT
private static final double X_CRITThe numberX_CRIT
is used byerf(double, double)
internally. This number solveserf(x)=0.5
within 1ulp. More precisely, the current implementations oferf(double)
anderfc(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:
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Constructor Details
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Erf
private Erf()Default constructor. Prohibit instantiation.
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Method Details
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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
, thenerf(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:
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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
, thenerf(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:
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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 valuex2
- the second value- Returns:
- erf(x2) - erf(x1)
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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
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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
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