statistics-0.14.0.2: A library of statistical types, data, and functions

Copyright(c) 2011 Bryan O'Sullivan
LicenseBSD3
Maintainerbos@serpentine.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

Statistics.Math.RootFinding

Contents

Description

Haskell functions for finding the roots of mathematical functions.

Synopsis

Documentation

data Root a Source #

The result of searching for a root of a mathematical function.

Constructors

NotBracketed

The function does not have opposite signs when evaluated at the lower and upper bounds of the search.

SearchFailed

The search failed to converge to within the given error tolerance after the given number of iterations.

Root a

A root was successfully found.

Instances

Monad Root Source # 

Methods

(>>=) :: Root a -> (a -> Root b) -> Root b #

(>>) :: Root a -> Root b -> Root b #

return :: a -> Root a #

fail :: String -> Root a #

Functor Root Source # 

Methods

fmap :: (a -> b) -> Root a -> Root b #

(<$) :: a -> Root b -> Root a #

Applicative Root Source # 

Methods

pure :: a -> Root a #

(<*>) :: Root (a -> b) -> Root a -> Root b #

(*>) :: Root a -> Root b -> Root b #

(<*) :: Root a -> Root b -> Root a #

Alternative Root Source # 

Methods

empty :: Root a #

(<|>) :: Root a -> Root a -> Root a #

some :: Root a -> Root [a] #

many :: Root a -> Root [a] #

MonadPlus Root Source # 

Methods

mzero :: Root a #

mplus :: Root a -> Root a -> Root a #

Eq a => Eq (Root a) Source # 

Methods

(==) :: Root a -> Root a -> Bool #

(/=) :: Root a -> Root a -> Bool #

Data a => Data (Root a) Source # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Root a -> c (Root a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Root a) #

toConstr :: Root a -> Constr #

dataTypeOf :: Root a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Root a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Root a)) #

gmapT :: (forall b. Data b => b -> b) -> Root a -> Root a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Root a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Root a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Root a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Root a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Root a -> m (Root a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Root a -> m (Root a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Root a -> m (Root a) #

Read a => Read (Root a) Source # 
Show a => Show (Root a) Source # 

Methods

showsPrec :: Int -> Root a -> ShowS #

show :: Root a -> String #

showList :: [Root a] -> ShowS #

Generic (Root a) Source # 

Associated Types

type Rep (Root a) :: * -> * #

Methods

from :: Root a -> Rep (Root a) x #

to :: Rep (Root a) x -> Root a #

ToJSON a => ToJSON (Root a) Source # 
FromJSON a => FromJSON (Root a) Source # 
Binary a => Binary (Root a) Source # 

Methods

put :: Root a -> Put #

get :: Get (Root a) #

putList :: [Root a] -> Put #

type Rep (Root a) Source # 
type Rep (Root a) = D1 (MetaData "Root" "Statistics.Math.RootFinding" "statistics-0.14.0.2-9wDz1lVU92ZDJSrAe5uHzb" False) ((:+:) (C1 (MetaCons "NotBracketed" PrefixI False) U1) ((:+:) (C1 (MetaCons "SearchFailed" PrefixI False) U1) (C1 (MetaCons "Root" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))))

fromRoot Source #

Arguments

:: a

Default value.

-> Root a

Result of search for a root.

-> a 

Returns either the result of a search for a root, or the default value if the search failed.

ridders Source #

Arguments

:: Double

Absolute error tolerance.

-> (Double, Double)

Lower and upper bounds for the search.

-> (Double -> Double)

Function to find the roots of.

-> Root Double 

Use the method of Ridders to compute a root of a function.

The function must have opposite signs when evaluated at the lower and upper bounds of the search (i.e. the root must be bracketed).

References

  • Ridders, C.F.J. (1979) A new algorithm for computing a single root of a real continuous function. IEEE Transactions on Circuits and Systems 26:979–980.