Safe Haskell	None
Language	Haskell98

Data.Number.Erf

Synopsis

class Floating a => Erf a where
- erf :: a -> a
- erfc :: a -> a
- erfcx :: a -> a
- normcdf :: a -> a
class Floating a => InvErf a where
- inverf :: a -> a
- inverfc :: a -> a
- invnormcdf :: a -> a

Documentation

class Floating a => Erf a where #

Error function related functions.

The derivative of erf is x -> 2 / sqrt pi * exp (x^2), and this uniquely determines erf by erf 0 = 0.

Minimal complete definition is erfc or normcdf.

Minimal complete definition

Nothing

Methods

erf :: a -> a #

erfc #

Arguments

:: a
-> a	erfc x = 1 - erf x

erfcx #

Arguments

:: a
-> a	erfcx x = exp (xx) erfc x

normcdf #

Arguments

:: a
-> a	normcdf x = erfc(-x sqrt 2) 2

Instances

Erf Double #
Instance details Defined in Data.Number.Erf Methods erf :: Double -> Double # erfc :: Double -> Double # erfcx :: Double -> Double # normcdf :: Double -> Double #
Erf Float #
Instance details Defined in Data.Number.Erf Methods erf :: Float -> Float # erfc :: Float -> Float # erfcx :: Float -> Float # normcdf :: Float -> Float #

class Floating a => InvErf a where #

Inverse error functions, e.g., inverf . erf = id and erf . inverf = id assuming the appropriate codomain for inverf. Note that the accuracy may drop radically for extreme arguments.

Minimal complete definition

invnormcdf

Methods

inverf :: a -> a #

inverfc :: a -> a #

invnormcdf :: a -> a #

Instances

InvErf Double #
Instance details Defined in Data.Number.Erf Methods inverf :: Double -> Double # inverfc :: Double -> Double # invnormcdf :: Double -> Double #
InvErf Float #
Instance details Defined in Data.Number.Erf Methods inverf :: Float -> Float # inverfc :: Float -> Float # invnormcdf :: Float -> Float #