math-functions-0.2.0.1: Special functions and Chebyshev polynomials

Numeric.RootFinding

Contents

Description

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

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

 Source # Methods(>>=) :: Root a -> (a -> Root b) -> Root b #(>>) :: Root a -> Root b -> Root b #return :: a -> Root a #fail :: String -> Root a # Source # Methodsfmap :: (a -> b) -> Root a -> Root b #(<\$) :: a -> Root b -> Root a # Source # Methodspure :: a -> Root a #(<*>) :: Root (a -> b) -> Root a -> Root b #(*>) :: Root a -> Root b -> Root b #(<*) :: Root a -> Root b -> Root a # Source # Methodsempty :: Root a #(<|>) :: Root a -> Root a -> Root a #some :: Root a -> Root [a] #many :: Root a -> Root [a] # Source # Methodsmzero :: 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 # Methodsgfoldl :: (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 # MethodsreadsPrec :: Int -> ReadS (Root a) #readList :: ReadS [Root a] # Show a => Show (Root a) Source # MethodsshowsPrec :: Int -> Root a -> ShowS #show :: Root a -> String #showList :: [Root a] -> ShowS # Generic (Root a) Source # Associated Typestype Rep (Root a) :: * -> * # Methodsfrom :: Root a -> Rep (Root a) x #to :: Rep (Root a) x -> Root a # type Rep (Root a) Source # type Rep (Root a) = D1 (MetaData "Root" "Numeric.RootFinding" "math-functions-0.2.0.1-5a7TAmALZ356fcJFgrBqk5" 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)))))

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.

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).

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.