Copyright	(c) 2011 Bryan O'Sullivan
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

Statistics.Math.RootFinding

Contents

References

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 #
Methods readsPrec :: Int -> ReadS (Root a) # readList :: ReadS [Root a] # readPrec :: ReadPrec (Root a) # readListPrec :: ReadPrec [Root a] #
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 #
Methods toJSON :: Root a -> Value # toEncoding :: Root a -> Encoding # toJSONList :: [Root a] -> Value # toEncodingList :: [Root a] -> Encoding #
FromJSON a => FromJSON (Root a) Source #
Methods parseJSON :: Value -> Parser (Root a) # parseJSONList :: Value -> Parser [Root a] #
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.