Copyright	(c) 2011 Bryan O'Sullivan
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Numeric.RootFinding

Contents

References

Description

Haskell functions for finding the roots of real functions of real arguments.

Synopsis

Documentation

data Root a #

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 #
Methods (>>=) :: Root a -> (a -> Root b) -> Root b # (>>) :: Root a -> Root b -> Root b # return :: a -> Root a # fail :: String -> Root a #
Functor Root #
Methods fmap :: (a -> b) -> Root a -> Root b # (<$) :: a -> Root b -> Root a #
Applicative Root #
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 #
Methods empty :: Root a # (<\|>) :: Root a -> Root a -> Root a # some :: Root a -> Root [a] # many :: Root a -> Root [a] #
MonadPlus Root #
Methods mzero :: Root a # mplus :: Root a -> Root a -> Root a #
Eq a => Eq (Root a) #
Methods (==) :: Root a -> Root a -> Bool # (/=) :: Root a -> Root a -> Bool #
Data a => Data (Root a) #
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) #
Methods readsPrec :: Int -> ReadS (Root a) # readList :: ReadS [Root a] # readPrec :: ReadPrec (Root a) # readListPrec :: ReadPrec [Root a] #
Show a => Show (Root a) #
Methods showsPrec :: Int -> Root a -> ShowS # show :: Root a -> String # showList :: [Root a] -> ShowS #
Generic (Root a) #
Associated Types type Rep (Root a) :: * -> * # Methods from :: Root a -> Rep (Root a) x # to :: Rep (Root a) x -> Root a #
type Rep (Root a) #
type Rep (Root a) = D1 (MetaData "Root" "Numeric.RootFinding" "math-functions-0.2.1.0-5HGc50cbfqADZLQ6JEdEhK" 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 #

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 #

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).

newtonRaphson #

Arguments

:: Double	Required precision
-> (Double, Double, Double)	(lower bound, initial guess, upper bound). Iterations will no go outside of the interval
-> (Double -> (Double, Double))	Function to finds roots. It returns pair of function value and its derivative
-> Root Double

Solve equation using Newton-Raphson iterations.

This method require both initial guess and bounds for root. If Newton step takes us out of bounds on root function reverts to bisection.

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.