Data.Number.Erf

erf-2.0.0.0: The error function, erf, and related functions.

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 (x*x) * erfc x

normcdf

Arguments

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

Instances

Erf Double |
Erf 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 |
InvErf Float |