Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Number.StreamInterface

Synopsis

class (Monad str, StreamBuilder str, StreamObserver str) => Limiting str a where
- data Closure str a
- limit :: str a -> Closure str a
- approximations :: Closure str a -> str a
class (Fractional a, Limiting str a) => Infinitesimal str a where
- epsilon_closure :: Closure str a
- infinite_closure :: Closure str a
- minus_infinite_closure :: Closure str a
- nan_closure :: Closure str a
- epsilon_stream :: str a
- infinite_stream :: str a
- minus_infinite_stream :: str a
class Applicative str => StreamBuilder str where
- pre :: a -> str a -> str a
class Applicative str => StreamObserver str where
- shead :: str a -> a
- stail :: str a -> str a
data Stream a = Pre {
- shead_impl :: a
- stail_lazy :: Stream a
}
class Infinitesimal Stream a => Closed a where
- accumulation_point :: Closure Stream a -> a
type DerivateConstraint str a = (Monad str, Num a)
partial_derivate :: (Closed eps, Fractional eps) => (eps -> a -> a) -> (a -> eps) -> a -> eps
partial_derive :: (Closed a, Infinitesimal Stream a, Fractional a) => (a -> a -> a) -> (a -> a) -> a -> a
derivate_around :: Infinitesimal str a => (a -> a) -> a -> Closure str a
vector_derivate :: (Infinitesimal str (Scalar a), VectorSpace a, Limiting str a) => (Scalar a -> a) -> Scalar a -> Closure str a
derivate_closed :: Infinitesimal str a => (a -> a) -> a -> Closure str a
newtons_method_real :: (Infinitesimal Stream a, Closed a) => (a -> a) -> a -> Closure Stream a
iterate_stream :: StreamBuilder str => (a -> a) -> a -> str a
pseudo_derivate :: (Fractional r, Limiting str r, Infinitesimal str a) => (a -> r) -> a -> Closure str r
partial_derivate1_2 :: Infinitesimal str a => (a -> b -> a) -> a -> b -> Closure str a
partial_derivate2_2 :: Infinitesimal str a => (b -> a -> a) -> b -> a -> Closure str a
partial_derivate1_3 :: Infinitesimal str a => (a -> b -> c -> a) -> a -> b -> c -> Closure str a
partial_derivate2_3 :: Infinitesimal str a => (b -> a -> c -> a) -> b -> a -> c -> Closure str a
partial_derivate3_3 :: Infinitesimal str a => (b -> c -> a -> a) -> b -> c -> a -> Closure str a
constant :: a -> Stream a
stream_matrix_impl :: Stream a -> Stream (Stream a, Stream a) -> (Stream :*: Stream) a
stream_diagonal_impl :: (Stream :*: Stream) a -> Stream a
stream_codiagonal_impl :: (Stream :*: Stream) a -> Stream (Stream a, Stream a)

Documentation

class (Monad str, StreamBuilder str, StreamObserver str) => Limiting str a where Source #

Idea: limit produces an exact value from a monotone sequence of approximations

https://ncatlab.org/nlab/show/closure+operator

The Closure represents a sequentially closed set of elements

Associated Types

data Closure str a Source #

Methods

limit :: str a -> Closure str a Source #

approximations :: Closure str a -> str a Source #

Instances

Instances details

Limiting Stream Rational Source #	https://en.wikipedia.org/wiki/Matrix_exponential
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Rational Source # Methods limit :: Stream Rational -> Closure Stream Rational Source # approximations :: Closure Stream Rational -> Stream Rational Source #
Limiting Stream R Source #
Instance details Defined in Math.Number.R Associated Types data Closure Stream R Source # Methods limit :: Stream R -> Closure Stream R Source # approximations :: Closure Stream R -> Stream R Source #
Limiting Stream R Source #	The following instance declaration represents the completeness of the real number system.
Instance details Defined in Math.Number.Real Associated Types data Closure Stream R Source # Methods limit :: Stream R -> Closure Stream R Source # approximations :: Closure Stream R -> Stream R Source #
Limiting Stream Integer Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Integer Source # Methods limit :: Stream Integer -> Closure Stream Integer Source # approximations :: Closure Stream Integer -> Stream Integer Source #
Limiting Stream Double Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Double Source # Methods limit :: Stream Double -> Closure Stream Double Source # approximations :: Closure Stream Double -> Stream Double Source #
Limiting Stream Float Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Float Source # Methods limit :: Stream Float -> Closure Stream Float Source # approximations :: Closure Stream Float -> Stream Float Source #
(Monad str, StreamObserver str, StreamBuilder str) => Limiting str Bool Source #
Instance details Defined in Math.Number.Real Associated Types data Closure str Bool Source # Methods limit :: str Bool -> Closure str Bool Source # approximations :: Closure str Bool -> str Bool Source #
(Show r, Limiting Stream r) => Limiting Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types data Closure Stream (Quantity r) Source # Methods limit :: Stream (Quantity r) -> Closure Stream (Quantity r) Source # approximations :: Closure Stream (Quantity r) -> Stream (Quantity r) Source #
(Num a, Limiting Stream a) => Limiting Stream (Stream a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (Stream a) Source # Methods limit :: Stream (Stream a) -> Closure Stream (Stream a) Source # approximations :: Closure Stream (Stream a) -> Stream (Stream a) Source #
Limiting Stream (IO ()) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (IO ()) Source # Methods limit :: Stream (IO ()) -> Closure Stream (IO ()) Source # approximations :: Closure Stream (IO ()) -> Stream (IO ()) Source #
Limiting str a => Limiting str (Complex a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure str (Complex a) Source # Methods limit :: str (Complex a) -> Closure str (Complex a) Source # approximations :: Closure str (Complex a) -> str (Complex a) Source #
Limiting str a => Limiting str (Vector1 a) Source #
Instance details Defined in Math.Matrix.Vector1 Associated Types data Closure str (Vector1 a) Source # Methods limit :: str (Vector1 a) -> Closure str (Vector1 a) Source # approximations :: Closure str (Vector1 a) -> str (Vector1 a) Source #
(Limiting str a, Monad str) => Limiting str (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types data Closure str (Vector2 a) Source # Methods limit :: str (Vector2 a) -> Closure str (Vector2 a) Source # approximations :: Closure str (Vector2 a) -> str (Vector2 a) Source #
(Monad str, Limiting str a) => Limiting str (Vector3 a) Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data Closure str (Vector3 a) Source # Methods limit :: str (Vector3 a) -> Closure str (Vector3 a) Source # approximations :: Closure str (Vector3 a) -> str (Vector3 a) Source #
(Monad str, Limiting str a) => Limiting str (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types data Closure str (Vector4 a) Source # Methods limit :: str (Vector4 a) -> Closure str (Vector4 a) Source # approximations :: Closure str (Vector4 a) -> str (Vector4 a) Source #
Limiting Stream (a :==: a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (a :==: a) Source # Methods limit :: Stream (a :==: a) -> Closure Stream (a :==: a) Source # approximations :: Closure Stream (a :==: a) -> Stream (a :==: a) Source #
(Limiting str a, Limiting str b) => Limiting str (a, b) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure str (a, b) Source # Methods limit :: str (a, b) -> Closure str (a, b) Source # approximations :: Closure str (a, b) -> str (a, b) Source #
Monad m => Limiting Stream (Kleisli m a a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (Kleisli m a a) Source # Methods limit :: Stream (Kleisli m a a) -> Closure Stream (Kleisli m a a) Source # approximations :: Closure Stream (Kleisli m a a) -> Stream (Kleisli m a a) Source #
(Limiting str a, Limiting str b, Limiting str c) => Limiting str (a, b, c) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure str (a, b, c) Source # Methods limit :: str (a, b, c) -> Closure str (a, b, c) Source # approximations :: Closure str (a, b, c) -> str (a, b, c) Source #
(Applicative f, Traversable f, Traversable str, Applicative g, Traversable g, Limiting str a) => Limiting str ((f :*: g) a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure str ((f :: g) a) Source # Methods limit :: str ((f :: g) a) -> Closure str ((f :: g) a) Source # approximations :: Closure str ((f :: g) a) -> str ((f :*: g) a) Source #

class (Fractional a, Limiting str a) => Infinitesimal str a where Source #

Minimal complete definition

(epsilon_closure | epsilon_stream)

Methods

epsilon_closure :: Closure str a Source #

infinite_closure :: Closure str a Source #

minus_infinite_closure :: Closure str a Source #

nan_closure :: Closure str a Source #

epsilon_stream :: str a Source #

infinite_stream :: str a Source #

minus_infinite_stream :: str a Source #

Instances

Instances details

Infinitesimal Stream Rational Source #
Instance details Defined in Math.Number.Real Methods epsilon_closure :: Closure Stream Rational Source # infinite_closure :: Closure Stream Rational Source # minus_infinite_closure :: Closure Stream Rational Source # nan_closure :: Closure Stream Rational Source # epsilon_stream :: Stream Rational Source # infinite_stream :: Stream Rational Source # minus_infinite_stream :: Stream Rational Source #
Infinitesimal Stream R Source #
Instance details Defined in Math.Number.R Methods epsilon_closure :: Closure Stream R Source # infinite_closure :: Closure Stream R Source # minus_infinite_closure :: Closure Stream R Source # nan_closure :: Closure Stream R Source # epsilon_stream :: Stream R Source # infinite_stream :: Stream R Source # minus_infinite_stream :: Stream R Source #
Infinitesimal Stream R Source #	epsilon is a real that converges to zero.
Instance details Defined in Math.Number.Real Methods epsilon_closure :: Closure Stream R Source # infinite_closure :: Closure Stream R Source # minus_infinite_closure :: Closure Stream R Source # nan_closure :: Closure Stream R Source # epsilon_stream :: Stream R Source # infinite_stream :: Stream R Source # minus_infinite_stream :: Stream R Source #
Infinitesimal Stream Double Source #	Notice that after double precision is not sufficient, the infinitesimals are zero.
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream Double Source # infinite_closure :: Closure Stream Double Source # minus_infinite_closure :: Closure Stream Double Source # nan_closure :: Closure Stream Double Source # epsilon_stream :: Stream Double Source # infinite_stream :: Stream Double Source # minus_infinite_stream :: Stream Double Source #
Infinitesimal Stream Float Source #	Notice that after float precision is not sufficient, the infinitesimals are zero.
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream Float Source # infinite_closure :: Closure Stream Float Source # minus_infinite_closure :: Closure Stream Float Source # nan_closure :: Closure Stream Float Source # epsilon_stream :: Stream Float Source # infinite_stream :: Stream Float Source # minus_infinite_stream :: Stream Float Source #
(Show r, Infinitesimal Stream r) => Infinitesimal Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods epsilon_closure :: Closure Stream (Quantity r) Source # infinite_closure :: Closure Stream (Quantity r) Source # minus_infinite_closure :: Closure Stream (Quantity r) Source # nan_closure :: Closure Stream (Quantity r) Source # epsilon_stream :: Stream (Quantity r) Source # infinite_stream :: Stream (Quantity r) Source # minus_infinite_stream :: Stream (Quantity r) Source #
(Infinitesimal Stream a, Num a) => Infinitesimal Stream (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream (Stream a) Source # infinite_closure :: Closure Stream (Stream a) Source # minus_infinite_closure :: Closure Stream (Stream a) Source # nan_closure :: Closure Stream (Stream a) Source # epsilon_stream :: Stream (Stream a) Source # infinite_stream :: Stream (Stream a) Source # minus_infinite_stream :: Stream (Stream a) Source #
(RealFloat a, Infinitesimal str a) => Infinitesimal str (Complex a) Source #
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure str (Complex a) Source # infinite_closure :: Closure str (Complex a) Source # minus_infinite_closure :: Closure str (Complex a) Source # nan_closure :: Closure str (Complex a) Source # epsilon_stream :: str (Complex a) Source # infinite_stream :: str (Complex a) Source # minus_infinite_stream :: str (Complex a) Source #
Infinitesimal str a => Infinitesimal str (Vector1 a) Source #
Instance details Defined in Math.Matrix.Vector1 Methods epsilon_closure :: Closure str (Vector1 a) Source # infinite_closure :: Closure str (Vector1 a) Source # minus_infinite_closure :: Closure str (Vector1 a) Source # nan_closure :: Closure str (Vector1 a) Source # epsilon_stream :: str (Vector1 a) Source # infinite_stream :: str (Vector1 a) Source # minus_infinite_stream :: str (Vector1 a) Source #

class Applicative str => StreamBuilder str where Source #

Methods

pre :: a -> str a -> str a infixr 5 Source #

Instances

Instances details

StreamBuilder Stream Source #
Instance details Defined in Math.Number.Stream Methods pre :: a -> Stream a -> Stream a Source #

class Applicative str => StreamObserver str where Source #

Methods

shead :: str a -> a Source #

stail :: str a -> str a Source #

Instances

Instances details

StreamObserver Stream Source #
Instance details Defined in Math.Number.StreamInterface Methods shead :: Stream a -> a Source # stail :: Stream a -> Stream a Source #

data Stream a Source #

Data structure of infinite lazy streams.

Constructors

Pre infixr 5
Fields shead_impl :: a stail_lazy :: Stream a

Instances

Instances details

MonadFail Stream Source #
Instance details Defined in Math.Number.Stream Methods fail :: String -> Stream a #
Foldable Stream Source #
Instance details Defined in Math.Number.Stream Methods fold :: Monoid m => Stream m -> m # foldMap :: Monoid m => (a -> m) -> Stream a -> m # foldMap' :: Monoid m => (a -> m) -> Stream a -> m # foldr :: (a -> b -> b) -> b -> Stream a -> b # foldr' :: (a -> b -> b) -> b -> Stream a -> b # foldl :: (b -> a -> b) -> b -> Stream a -> b # foldl' :: (b -> a -> b) -> b -> Stream a -> b # foldr1 :: (a -> a -> a) -> Stream a -> a # foldl1 :: (a -> a -> a) -> Stream a -> a # toList :: Stream a -> [a] # null :: Stream a -> Bool # length :: Stream a -> Int # elem :: Eq a => a -> Stream a -> Bool # maximum :: Ord a => Stream a -> a # minimum :: Ord a => Stream a -> a # sum :: Num a => Stream a -> a # product :: Num a => Stream a -> a #
Traversable Stream Source #
Instance details Defined in Math.Number.Stream Methods traverse :: Applicative f => (a -> f b) -> Stream a -> f (Stream b) # sequenceA :: Applicative f => Stream (f a) -> f (Stream a) # mapM :: Monad m => (a -> m b) -> Stream a -> m (Stream b) # sequence :: Monad m => Stream (m a) -> m (Stream a) #
Applicative Stream Source #
Instance details Defined in Math.Number.StreamInterface Methods pure :: a -> Stream a # (<>) :: Stream (a -> b) -> Stream a -> Stream b # liftA2 :: (a -> b -> c) -> Stream a -> Stream b -> Stream c # (>) :: Stream a -> Stream b -> Stream b # (<*) :: Stream a -> Stream b -> Stream a #
Functor Stream Source #
Instance details Defined in Math.Number.StreamInterface Methods fmap :: (a -> b) -> Stream a -> Stream b # (<$) :: a -> Stream b -> Stream a #
Monad Stream Source #	According to http://patternsinfp.wordpress.com/2010/12/31/stream-monad/, the diagonal is the join of the stream monad.
Instance details Defined in Math.Number.Stream Methods (>>=) :: Stream a -> (a -> Stream b) -> Stream b # (>>) :: Stream a -> Stream b -> Stream b # return :: a -> Stream a #
StreamBuilder Stream Source #
Instance details Defined in Math.Number.Stream Methods pre :: a -> Stream a -> Stream a Source #
StreamObserver Stream Source #
Instance details Defined in Math.Number.StreamInterface Methods shead :: Stream a -> a Source # stail :: Stream a -> Stream a Source #
CircularComonad Stream Source #
Instance details Defined in Math.Number.Stream Methods rotate :: Stream a -> Stream a Source #
Comonad Stream Source #
Instance details Defined in Math.Number.Stream Methods extract :: Stream a -> a Source # duplicate :: Stream a -> Stream (Stream a) Source # extend :: (Stream a -> b) -> Stream a -> Stream b Source # (=>>) :: Stream a -> (Stream a -> b) -> Stream b Source # (.>>) :: Stream a -> b -> Stream b Source #
InfiniteComonad Stream Source #
Instance details Defined in Math.Number.Stream Methods comonad_pre :: a -> Stream a -> Stream a Source #
InterleaveFunctor Stream Source #
Instance details Defined in Math.Number.Stream Methods interleave :: Stream a -> Stream a -> Stream a Source #
Nondeterministic Stream Source #
Instance details Defined in Math.Number.Stream Methods guess :: [a] -> Stream a Source #
PpShowF Stream Source #
Instance details Defined in Math.Number.Stream Methods ppf :: PpShow a => Stream a -> Doc Source #
PpShowVerticalF Stream Source #
Instance details Defined in Math.Number.Stream Methods ppf_vertical :: PpShow a => Stream a -> Doc Source #
AppendableVector Vector2 Stream Source #
Instance details Defined in Math.Matrix.VectorConversions Associated Types type Vector2 :+: Stream :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Stream a -> (Vector2 :+: Stream) a Source #
AppendableVector Vector3 Stream Source #
Instance details Defined in Math.Number.Stream Associated Types type Vector3 :+: Stream :: Type -> Type Source # Methods (\|\|>>) :: Vector3 a -> Stream a -> (Vector3 :+: Stream) a Source #
Num a => CodiagonalMatrix Stream a Source #
Instance details Defined in Math.Number.StreamInterface Associated Types data Codiagonal Stream a Source # type Stream \\ a Source # Methods codiagonal_impl :: (Stream :: Stream) a -> Codiagonal Stream a Source # (\|\\|) :: Stream a -> Codiagonal Stream a -> (Stream :: Stream) a Source # down_project :: Codiagonal Stream a -> Stream \\ a Source # right_project :: Codiagonal Stream a -> Stream \\ a Source #
Num a => Diagonalizable Stream a Source #	square matrix implementation for streams.
Instance details Defined in Math.Number.Stream Methods identity_impl :: Stream Integer -> (Stream :: Stream) a Source # identity :: (Stream :: Stream) a Source # diagonal_impl :: (Stream :: Stream) a -> Stream a Source # diagonal_matrix_impl :: Stream a -> (Stream :: Stream) a Source #
Num a => Indexable Stream a Source #
Instance details Defined in Math.Number.Stream Methods diagonal_projections :: Stream (Index Stream a) Source # basis_vector :: Index Stream a -> Stream a Source # index_project :: Index Stream a -> Stream a -> a Source # indexable_indices :: Stream a Source #
Approximations Stream R Source #
Instance details Defined in Math.Number.R Methods floating_approximations :: R -> Stream Double Source # rational_approximations :: R -> Stream Rational Source #
Approximations Stream R Source #
Instance details Defined in Math.Number.Real Methods floating_approximations :: R -> Stream Double Source # rational_approximations :: R -> Stream Rational Source #
Approximations Stream Double Source #
Instance details Defined in Math.Number.Stream Methods floating_approximations :: Double -> Stream Double Source # rational_approximations :: Double -> Stream Rational Source #
Approximations Stream Float Source #
Instance details Defined in Math.Number.Stream Methods floating_approximations :: Float -> Stream Double Source # rational_approximations :: Float -> Stream Rational Source #
Infinitesimal Stream Rational Source #
Instance details Defined in Math.Number.Real Methods epsilon_closure :: Closure Stream Rational Source # infinite_closure :: Closure Stream Rational Source # minus_infinite_closure :: Closure Stream Rational Source # nan_closure :: Closure Stream Rational Source # epsilon_stream :: Stream Rational Source # infinite_stream :: Stream Rational Source # minus_infinite_stream :: Stream Rational Source #
Infinitesimal Stream R Source #
Instance details Defined in Math.Number.R Methods epsilon_closure :: Closure Stream R Source # infinite_closure :: Closure Stream R Source # minus_infinite_closure :: Closure Stream R Source # nan_closure :: Closure Stream R Source # epsilon_stream :: Stream R Source # infinite_stream :: Stream R Source # minus_infinite_stream :: Stream R Source #
Infinitesimal Stream R Source #	epsilon is a real that converges to zero.
Instance details Defined in Math.Number.Real Methods epsilon_closure :: Closure Stream R Source # infinite_closure :: Closure Stream R Source # minus_infinite_closure :: Closure Stream R Source # nan_closure :: Closure Stream R Source # epsilon_stream :: Stream R Source # infinite_stream :: Stream R Source # minus_infinite_stream :: Stream R Source #
Infinitesimal Stream Double Source #	Notice that after double precision is not sufficient, the infinitesimals are zero.
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream Double Source # infinite_closure :: Closure Stream Double Source # minus_infinite_closure :: Closure Stream Double Source # nan_closure :: Closure Stream Double Source # epsilon_stream :: Stream Double Source # infinite_stream :: Stream Double Source # minus_infinite_stream :: Stream Double Source #
Infinitesimal Stream Float Source #	Notice that after float precision is not sufficient, the infinitesimals are zero.
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream Float Source # infinite_closure :: Closure Stream Float Source # minus_infinite_closure :: Closure Stream Float Source # nan_closure :: Closure Stream Float Source # epsilon_stream :: Stream Float Source # infinite_stream :: Stream Float Source # minus_infinite_stream :: Stream Float Source #
Limiting Stream Rational Source #	https://en.wikipedia.org/wiki/Matrix_exponential
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Rational Source # Methods limit :: Stream Rational -> Closure Stream Rational Source # approximations :: Closure Stream Rational -> Stream Rational Source #
Limiting Stream R Source #
Instance details Defined in Math.Number.R Associated Types data Closure Stream R Source # Methods limit :: Stream R -> Closure Stream R Source # approximations :: Closure Stream R -> Stream R Source #
Limiting Stream R Source #	The following instance declaration represents the completeness of the real number system.
Instance details Defined in Math.Number.Real Associated Types data Closure Stream R Source # Methods limit :: Stream R -> Closure Stream R Source # approximations :: Closure Stream R -> Stream R Source #
Limiting Stream Integer Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Integer Source # Methods limit :: Stream Integer -> Closure Stream Integer Source # approximations :: Closure Stream Integer -> Stream Integer Source #
Limiting Stream Double Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Double Source # Methods limit :: Stream Double -> Closure Stream Double Source # approximations :: Closure Stream Double -> Stream Double Source #
Limiting Stream Float Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream Float Source # Methods limit :: Stream Float -> Closure Stream Float Source # approximations :: Closure Stream Float -> Stream Float Source #
Adjunction StreamIndex Stream Source #
Instance details Defined in Math.Number.Stream Methods leftAdjunct :: (StreamIndex a -> b) -> a -> Stream b Source # unit :: a -> Stream (StreamIndex a) Source # rightAdjunct :: (a -> Stream b) -> StreamIndex a -> b Source # counit :: StreamIndex (Stream b) -> b Source #
(Closed a, ConjugateSymmetric a, Num a) => LinearTransform Stream Stream a Source #
Instance details Defined in Math.Number.Stream Methods (<>>) :: Stream a -> (Stream :: Stream) a -> Stream a Source # (<<>) :: (Stream :: Stream) a -> Stream a -> Stream a Source #
Transposable Stream Vector1 a Source #
Instance details Defined in Math.Matrix.Vector1 Methods transpose_impl :: (Stream :: Vector1) a -> (Vector1 :: Stream) a Source #
Transposable Stream Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transpose_impl :: (Stream :: Vector2) a -> (Vector2 :: Stream) a Source #
Transposable Stream Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transpose_impl :: (Stream :: Vector3) a -> (Vector3 :: Stream) a Source #
Transposable Stream Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods transpose_impl :: (Stream :: Vector4) a -> (Vector4 :: Stream) a Source #
Num a => Transposable Stream Stream a Source #
Instance details Defined in Math.Number.StreamInterface Methods transpose_impl :: (Stream :: Stream) a -> (Stream :: Stream) a Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector1 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector1 a) (Stream a) -> (Vector1 :: Stream) a Source # linear :: (Vector1 :: Stream) a -> LinearMap (Vector1 a) (Stream a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Stream a) -> (Vector2 :: Stream) a Source # linear :: (Vector2 :: Stream) a -> LinearMap (Vector2 a) (Stream a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Stream a) -> (Vector3 :: Stream) a Source # linear :: (Vector3 :: Stream) a -> LinearMap (Vector3 a) (Stream a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Stream a) -> (Vector4 :: Stream) a Source # linear :: (Vector4 :: Stream) a -> LinearMap (Vector4 a) (Stream a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector1 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector1 a) -> (Stream :: Vector1) a Source # linear :: (Stream :: Vector1) a -> LinearMap (Stream a) (Vector1 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector2 a) -> (Stream :: Vector2) a Source # linear :: (Stream :: Vector2) a -> LinearMap (Stream a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector3 a) -> (Stream :: Vector3) a Source # linear :: (Stream :: Vector3) a -> LinearMap (Stream a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector4 a) -> (Stream :: Vector4) a Source # linear :: (Stream :: Vector4) a -> LinearMap (Stream a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a, Diagonalizable Stream a, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Stream a) -> (Stream :: Stream) a Source # linear :: (Stream :: Stream) a -> LinearMap (Stream a) (Stream a) Source #
(Show r, Infinitesimal Stream r) => Infinitesimal Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods epsilon_closure :: Closure Stream (Quantity r) Source # infinite_closure :: Closure Stream (Quantity r) Source # minus_infinite_closure :: Closure Stream (Quantity r) Source # nan_closure :: Closure Stream (Quantity r) Source # epsilon_stream :: Stream (Quantity r) Source # infinite_stream :: Stream (Quantity r) Source # minus_infinite_stream :: Stream (Quantity r) Source #
(Infinitesimal Stream a, Num a) => Infinitesimal Stream (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods epsilon_closure :: Closure Stream (Stream a) Source # infinite_closure :: Closure Stream (Stream a) Source # minus_infinite_closure :: Closure Stream (Stream a) Source # nan_closure :: Closure Stream (Stream a) Source # epsilon_stream :: Stream (Stream a) Source # infinite_stream :: Stream (Stream a) Source # minus_infinite_stream :: Stream (Stream a) Source #
(Show r, Limiting Stream r) => Limiting Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types data Closure Stream (Quantity r) Source # Methods limit :: Stream (Quantity r) -> Closure Stream (Quantity r) Source # approximations :: Closure Stream (Quantity r) -> Stream (Quantity r) Source #
(Num a, Limiting Stream a) => Limiting Stream (Stream a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (Stream a) Source # Methods limit :: Stream (Stream a) -> Closure Stream (Stream a) Source # approximations :: Closure Stream (Stream a) -> Stream (Stream a) Source #
Limiting Stream (IO ()) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (IO ()) Source # Methods limit :: Stream (IO ()) -> Closure Stream (IO ()) Source # approximations :: Closure Stream (IO ()) -> Stream (IO ()) Source #
Limiting Stream (a :==: a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (a :==: a) Source # Methods limit :: Stream (a :==: a) -> Closure Stream (a :==: a) Source # approximations :: Closure Stream (a :==: a) -> Stream (a :==: a) Source #
Monad m => Limiting Stream (Kleisli m a a) Source #
Instance details Defined in Math.Number.Stream Associated Types data Closure Stream (Kleisli m a a) Source # Methods limit :: Stream (Kleisli m a a) -> Closure Stream (Kleisli m a a) Source # approximations :: Closure Stream (Kleisli m a a) -> Stream (Kleisli m a a) Source #
Data a => Data (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Stream a -> c (Stream a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Stream a) # toConstr :: Stream a -> Constr # dataTypeOf :: Stream a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Stream a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Stream a)) # gmapT :: (forall b. Data b => b -> b) -> Stream a -> Stream a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Stream a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Stream a -> r # gmapQ :: (forall d. Data d => d -> u) -> Stream a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Stream a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Stream a -> m (Stream a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Stream a -> m (Stream a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Stream a -> m (Stream a) #
Monoid a => Monoid (Stream a) Source #	monoid instance for streams generated by monoid instance of the elements.
Instance details Defined in Math.Number.Stream Methods mempty :: Stream a # mappend :: Stream a -> Stream a -> Stream a # mconcat :: [Stream a] -> Stream a #
Semigroup a => Semigroup (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods (<>) :: Stream a -> Stream a -> Stream a # sconcat :: NonEmpty (Stream a) -> Stream a # stimes :: Integral b => b -> Stream a -> Stream a #
(Enum a, Num a) => Enum (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods succ :: Stream a -> Stream a # pred :: Stream a -> Stream a # toEnum :: Int -> Stream a # fromEnum :: Stream a -> Int # enumFrom :: Stream a -> [Stream a] # enumFromThen :: Stream a -> Stream a -> [Stream a] # enumFromTo :: Stream a -> Stream a -> [Stream a] # enumFromThenTo :: Stream a -> Stream a -> Stream a -> [Stream a] #
(ConjugateSymmetric a, Closed a, Eq a, Floating a) => Floating (Stream a) Source #	inverse trigonometric functions hyperbolic function
Instance details Defined in Math.Number.Stream Methods pi :: Stream a # exp :: Stream a -> Stream a # log :: Stream a -> Stream a # sqrt :: Stream a -> Stream a # (**) :: Stream a -> Stream a -> Stream a # logBase :: Stream a -> Stream a -> Stream a # sin :: Stream a -> Stream a # cos :: Stream a -> Stream a # tan :: Stream a -> Stream a # asin :: Stream a -> Stream a # acos :: Stream a -> Stream a # atan :: Stream a -> Stream a # sinh :: Stream a -> Stream a # cosh :: Stream a -> Stream a # tanh :: Stream a -> Stream a # asinh :: Stream a -> Stream a # acosh :: Stream a -> Stream a # atanh :: Stream a -> Stream a # log1p :: Stream a -> Stream a # expm1 :: Stream a -> Stream a # log1pexp :: Stream a -> Stream a # log1mexp :: Stream a -> Stream a #
Generic (Stream a) Source #
Instance details Defined in Math.Number.Stream Associated Types type Rep (Stream a) :: Type -> Type # Methods from :: Stream a -> Rep (Stream a) x # to :: Rep (Stream a) x -> Stream a #
Num a => Num (Stream a) Source #	Interpretation of a stream as a polynomial (its ordinary generating function) \[OGF_{s}(z) = \sum_{i=0}^{\infty}s_iz^i\] Good exposition exists in http://en.wikipedia.org/wiki/Formal_power_series the (*) operation is specific to ordinary generating function interpretation, i.e. discrete convolution/Cauchy product \[(xy)_k = \sum_{i+j=k}x_iy_j\] \[OGF_{xy}(z) = \sum_{k=0}^{\infty}\sum_{i+j=k}x_iy_jz^k\]
Instance details Defined in Math.Number.Stream Methods (+) :: Stream a -> Stream a -> Stream a # (-) :: Stream a -> Stream a -> Stream a # (*) :: Stream a -> Stream a -> Stream a # negate :: Stream a -> Stream a # abs :: Stream a -> Stream a # signum :: Stream a -> Stream a # fromInteger :: Integer -> Stream a #
Fractional a => Fractional (Stream a) Source #	Fractional instance is based on interpretation of a stream as generating function.
Instance details Defined in Math.Number.Stream Methods (/) :: Stream a -> Stream a -> Stream a # recip :: Stream a -> Stream a # fromRational :: Rational -> Stream a #
Integral a => Integral (Stream a) Source #	Integral instance is based on interpretation of a stream as generating function.
Instance details Defined in Math.Number.Stream Methods quot :: Stream a -> Stream a -> Stream a # rem :: Stream a -> Stream a -> Stream a # div :: Stream a -> Stream a -> Stream a # mod :: Stream a -> Stream a -> Stream a # quotRem :: Stream a -> Stream a -> (Stream a, Stream a) # divMod :: Stream a -> Stream a -> (Stream a, Stream a) # toInteger :: Stream a -> Integer #
(Num a, Ord a, Real a) => Real (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods toRational :: Stream a -> Rational #
Show a => Show (ComplexStream a) Source #
Instance details Defined in Math.Number.Complex Methods showsPrec :: Int -> ComplexStream a -> ShowS # show :: ComplexStream a -> String # showList :: [ComplexStream a] -> ShowS #
Show x => Show (Stream x) Source #	Show instance displays 15 elements from beginning of stream To display more elements, use `drop` operation.
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Stream x -> ShowS # show :: Stream x -> String # showList :: [Stream x] -> ShowS #
ConjugateSymmetric a => ConjugateSymmetric (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods conj :: Stream a -> Stream a Source #
(ConjugateSymmetric a, Num a, Closed a) => InnerProductSpace (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods (%.) :: Stream a -> Stream a -> Scalar (Stream a) Source #
MetricSpace (Stream R) Source #
Instance details Defined in Math.Number.Real Methods distance :: Stream R -> Stream R -> Scalar (Stream R) Source #
(Closed a, ConjugateSymmetric a, Floating a) => NormedSpace (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods norm :: Stream a -> Scalar (Stream a) Source # norm_squared :: Stream a -> Scalar (Stream a) Source #
Num a => VectorSpace (Stream a) Source #
Instance details Defined in Math.Number.StreamInterface Associated Types type Scalar (Stream a) Source # Methods vzero :: Stream a Source # vnegate :: Stream a -> Stream a Source # (%+) :: Stream a -> Stream a -> Stream a Source # (%*) :: Scalar (Stream a) -> Stream a -> Stream a Source #
(Closed a, Num a) => Closed (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods accumulation_point :: Closure Stream (Stream a) -> Stream a Source #
PpShow x => PpShow (Stream x) Source #	pretty printing displays 15 element prefix of the stream.
Instance details Defined in Math.Number.Stream Methods pp :: Stream x -> Doc Source #
Builder a => Builder (Stream a) Source #	unfold for streams
Instance details Defined in Math.Number.Stream Associated Types data Unfold (Stream a) :: Type -> Type Source # Methods build :: Unfold (Stream a) a0 -> a0 -> Stream a Source #
Visitor (Stream a) Source #	folds over streams
Instance details Defined in Math.Number.Stream Associated Types data Fold (Stream a) :: Type -> Type Source # Methods visit :: Fold (Stream a) a0 -> Stream a -> a0 Source #
Eq a => Eq (Stream a) Source #	The instance of Eq is kind of bogus, because equality for streams is only semidecidable. It's still possible to use this if you know that the operation on your specific streams terminate. worst case occurs if the streams contain exactly equal elements.
Instance details Defined in Math.Number.Stream Methods (==) :: Stream a -> Stream a -> Bool # (/=) :: Stream a -> Stream a -> Bool #
Ord a => Ord (Stream a) Source #	this instance of Ord goes to infinite loop if the compared streams are equal.
Instance details Defined in Math.Number.Stream Methods compare :: Stream a -> Stream a -> Ordering # (<) :: Stream a -> Stream a -> Bool # (<=) :: Stream a -> Stream a -> Bool # (>) :: Stream a -> Stream a -> Bool # (>=) :: Stream a -> Stream a -> Bool # max :: Stream a -> Stream a -> Stream a # min :: Stream a -> Stream a -> Stream a #
Num a => DecomposableVectorSpace (Stream a) ((->) Integer) Source #
Instance details Defined in Math.Matrix.Simple Methods decompose :: (Scalar (Stream a) -> res) -> Stream a -> Integer -> res Source # project :: Stream a -> Integer -> Scalar (Stream a) Source #
(Show (Closure Stream r), Floating (Closure Stream r)) => Floating (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pi :: Closure Stream (Quantity r) # exp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sqrt :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (**) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # logBase :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sin :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # cos :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # tan :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # asin :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # acos :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # atan :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sinh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # cosh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # tanh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # asinh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # acosh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # atanh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1p :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # expm1 :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1pexp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1mexp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) #
Floating (Closure Stream R) Source #
Instance details Defined in Math.Number.R Methods pi :: Closure Stream R # exp :: Closure Stream R -> Closure Stream R # log :: Closure Stream R -> Closure Stream R # sqrt :: Closure Stream R -> Closure Stream R # (**) :: Closure Stream R -> Closure Stream R -> Closure Stream R # logBase :: Closure Stream R -> Closure Stream R -> Closure Stream R # sin :: Closure Stream R -> Closure Stream R # cos :: Closure Stream R -> Closure Stream R # tan :: Closure Stream R -> Closure Stream R # asin :: Closure Stream R -> Closure Stream R # acos :: Closure Stream R -> Closure Stream R # atan :: Closure Stream R -> Closure Stream R # sinh :: Closure Stream R -> Closure Stream R # cosh :: Closure Stream R -> Closure Stream R # tanh :: Closure Stream R -> Closure Stream R # asinh :: Closure Stream R -> Closure Stream R # acosh :: Closure Stream R -> Closure Stream R # atanh :: Closure Stream R -> Closure Stream R # log1p :: Closure Stream R -> Closure Stream R # expm1 :: Closure Stream R -> Closure Stream R # log1pexp :: Closure Stream R -> Closure Stream R # log1mexp :: Closure Stream R -> Closure Stream R #
Floating (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods pi :: Closure Stream R # exp :: Closure Stream R -> Closure Stream R # log :: Closure Stream R -> Closure Stream R # sqrt :: Closure Stream R -> Closure Stream R # (**) :: Closure Stream R -> Closure Stream R -> Closure Stream R # logBase :: Closure Stream R -> Closure Stream R -> Closure Stream R # sin :: Closure Stream R -> Closure Stream R # cos :: Closure Stream R -> Closure Stream R # tan :: Closure Stream R -> Closure Stream R # asin :: Closure Stream R -> Closure Stream R # acos :: Closure Stream R -> Closure Stream R # atan :: Closure Stream R -> Closure Stream R # sinh :: Closure Stream R -> Closure Stream R # cosh :: Closure Stream R -> Closure Stream R # tanh :: Closure Stream R -> Closure Stream R # asinh :: Closure Stream R -> Closure Stream R # acosh :: Closure Stream R -> Closure Stream R # atanh :: Closure Stream R -> Closure Stream R # log1p :: Closure Stream R -> Closure Stream R # expm1 :: Closure Stream R -> Closure Stream R # log1pexp :: Closure Stream R -> Closure Stream R # log1mexp :: Closure Stream R -> Closure Stream R #
(Show (Closure Stream a), RealFloat (Closure Stream a)) => RealFloat (Closure Stream (Quantity a)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods floatRadix :: Closure Stream (Quantity a) -> Integer # floatDigits :: Closure Stream (Quantity a) -> Int # floatRange :: Closure Stream (Quantity a) -> (Int, Int) # decodeFloat :: Closure Stream (Quantity a) -> (Integer, Int) # encodeFloat :: Integer -> Int -> Closure Stream (Quantity a) # exponent :: Closure Stream (Quantity a) -> Int # significand :: Closure Stream (Quantity a) -> Closure Stream (Quantity a) # scaleFloat :: Int -> Closure Stream (Quantity a) -> Closure Stream (Quantity a) # isNaN :: Closure Stream (Quantity a) -> Bool # isInfinite :: Closure Stream (Quantity a) -> Bool # isDenormalized :: Closure Stream (Quantity a) -> Bool # isNegativeZero :: Closure Stream (Quantity a) -> Bool # isIEEE :: Closure Stream (Quantity a) -> Bool # atan2 :: Closure Stream (Quantity a) -> Closure Stream (Quantity a) -> Closure Stream (Quantity a) #
(Closed a, Fractional a, ConjugateSymmetric a) => Num (Stream a :-> Stream a) Source #
Instance details Defined in Math.Number.Stream Methods (+) :: (Stream a :-> Stream a) -> (Stream a :-> Stream a) -> Stream a :-> Stream a # (-) :: (Stream a :-> Stream a) -> (Stream a :-> Stream a) -> Stream a :-> Stream a # (*) :: (Stream a :-> Stream a) -> (Stream a :-> Stream a) -> Stream a :-> Stream a # negate :: (Stream a :-> Stream a) -> Stream a :-> Stream a # abs :: (Stream a :-> Stream a) -> Stream a :-> Stream a # signum :: (Stream a :-> Stream a) -> Stream a :-> Stream a # fromInteger :: Integer -> Stream a :-> Stream a #
(Limiting Stream a, RealFloat a) => Num (Closure Stream (Complex a)) Source #
Instance details Defined in Math.Number.Stream Methods (+) :: Closure Stream (Complex a) -> Closure Stream (Complex a) -> Closure Stream (Complex a) # (-) :: Closure Stream (Complex a) -> Closure Stream (Complex a) -> Closure Stream (Complex a) # (*) :: Closure Stream (Complex a) -> Closure Stream (Complex a) -> Closure Stream (Complex a) # negate :: Closure Stream (Complex a) -> Closure Stream (Complex a) # abs :: Closure Stream (Complex a) -> Closure Stream (Complex a) # signum :: Closure Stream (Complex a) -> Closure Stream (Complex a) # fromInteger :: Integer -> Closure Stream (Complex a) #
Num (Closure Stream Rational) Source #
Instance details Defined in Math.Number.Stream Methods (+) :: Closure Stream Rational -> Closure Stream Rational -> Closure Stream Rational # (-) :: Closure Stream Rational -> Closure Stream Rational -> Closure Stream Rational # (*) :: Closure Stream Rational -> Closure Stream Rational -> Closure Stream Rational # negate :: Closure Stream Rational -> Closure Stream Rational # abs :: Closure Stream Rational -> Closure Stream Rational # signum :: Closure Stream Rational -> Closure Stream Rational # fromInteger :: Integer -> Closure Stream Rational #
(Show (Closure Stream r), Num (Closure Stream r)) => Num (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (+) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (-) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (*) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # negate :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # abs :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # signum :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # fromInteger :: Integer -> Closure Stream (Quantity r) #
Num (Closure Stream R) Source #
Instance details Defined in Math.Number.R Methods (+) :: Closure Stream R -> Closure Stream R -> Closure Stream R # (-) :: Closure Stream R -> Closure Stream R -> Closure Stream R # (*) :: Closure Stream R -> Closure Stream R -> Closure Stream R # negate :: Closure Stream R -> Closure Stream R # abs :: Closure Stream R -> Closure Stream R # signum :: Closure Stream R -> Closure Stream R # fromInteger :: Integer -> Closure Stream R #
Num (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods (+) :: Closure Stream R -> Closure Stream R -> Closure Stream R # (-) :: Closure Stream R -> Closure Stream R -> Closure Stream R # (*) :: Closure Stream R -> Closure Stream R -> Closure Stream R # negate :: Closure Stream R -> Closure Stream R # abs :: Closure Stream R -> Closure Stream R # signum :: Closure Stream R -> Closure Stream R # fromInteger :: Integer -> Closure Stream R #
Num (Closure Stream Integer) Source #
Instance details Defined in Math.Number.Stream Methods (+) :: Closure Stream Integer -> Closure Stream Integer -> Closure Stream Integer # (-) :: Closure Stream Integer -> Closure Stream Integer -> Closure Stream Integer # (*) :: Closure Stream Integer -> Closure Stream Integer -> Closure Stream Integer # negate :: Closure Stream Integer -> Closure Stream Integer # abs :: Closure Stream Integer -> Closure Stream Integer # signum :: Closure Stream Integer -> Closure Stream Integer # fromInteger :: Integer -> Closure Stream Integer #
Fractional (Closure Stream Rational) Source #
Instance details Defined in Math.Number.Stream Methods (/) :: Closure Stream Rational -> Closure Stream Rational -> Closure Stream Rational # recip :: Closure Stream Rational -> Closure Stream Rational # fromRational :: Rational -> Closure Stream Rational #
(Show (Closure Stream r), Fractional (Closure Stream r)) => Fractional (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (/) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # recip :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # fromRational :: Rational -> Closure Stream (Quantity r) #
Fractional (Closure Stream R) Source #
Instance details Defined in Math.Number.R Methods (/) :: Closure Stream R -> Closure Stream R -> Closure Stream R # recip :: Closure Stream R -> Closure Stream R # fromRational :: Rational -> Closure Stream R #
Fractional (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods (/) :: Closure Stream R -> Closure Stream R -> Closure Stream R # recip :: Closure Stream R -> Closure Stream R # fromRational :: Rational -> Closure Stream R #
(Show (Closure Stream r), Real (Closure Stream r)) => Real (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods toRational :: Closure Stream (Quantity r) -> Rational #
(Show (Closure Stream r), RealFrac (Closure Stream r)) => RealFrac (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods properFraction :: Integral b => Closure Stream (Quantity r) -> (b, Closure Stream (Quantity r)) # truncate :: Integral b => Closure Stream (Quantity r) -> b # round :: Integral b => Closure Stream (Quantity r) -> b # ceiling :: Integral b => Closure Stream (Quantity r) -> b # floor :: Integral b => Closure Stream (Quantity r) -> b #
Show (Closure Stream Rational) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Closure Stream Rational -> ShowS # show :: Closure Stream Rational -> String # showList :: [Closure Stream Rational] -> ShowS #
(ShowPrecision r, Show (Closure Stream r), Floating r, Ord r) => Show (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Closure Stream (Quantity r) -> ShowS # show :: Closure Stream (Quantity r) -> String # showList :: [Closure Stream (Quantity r)] -> ShowS #
Show (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods showsPrec :: Int -> Closure Stream R -> ShowS # show :: Closure Stream R -> String # showList :: [Closure Stream R] -> ShowS #
Show (Closure Stream a) => Show (Closure Stream (Stream a)) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Closure Stream (Stream a) -> ShowS # show :: Closure Stream (Stream a) -> String # showList :: [Closure Stream (Stream a)] -> ShowS #
Show (Closure Stream Integer) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Closure Stream Integer -> ShowS # show :: Closure Stream Integer -> String # showList :: [Closure Stream Integer] -> ShowS #
Show (Closure Stream Double) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Closure Stream Double -> ShowS # show :: Closure Stream Double -> String # showList :: [Closure Stream Double] -> ShowS #
Show (Closure Stream Float) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> Closure Stream Float -> ShowS # show :: Closure Stream Float -> String # showList :: [Closure Stream Float] -> ShowS #
(Closed a, Num a, ConjugateSymmetric a) => ConjugateSymmetric (Stream a :-> Stream a) Source #
Instance details Defined in Math.Number.Stream Methods conj :: (Stream a :-> Stream a) -> Stream a :-> Stream a Source #
ConjugateSymmetric (Closure Stream R) Source #
Instance details Defined in Math.Number.R Methods conj :: Closure Stream R -> Closure Stream R Source #
MetricSpace (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods distance :: Closure Stream R -> Closure Stream R -> Scalar (Closure Stream R) Source #
VectorSpace (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Associated Types type Scalar (Closure Stream R) Source # Methods vzero :: Closure Stream R Source # vnegate :: Closure Stream R -> Closure Stream R Source # (%+) :: Closure Stream R -> Closure Stream R -> Closure Stream R Source # (%*) :: Scalar (Closure Stream R) -> Closure Stream R -> Closure Stream R Source #
DifferentiallyClosed (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods derivate :: (Closure Stream R -> Closure Stream R) -> Closure Stream R -> Closure Stream R Source # integral :: (Closure Stream R, Closure Stream R) -> (Closure Stream R -> Closure Stream R) -> Closure Stream R Source #
Infinitary (Closure Stream Rational) Source #
Instance details Defined in Math.Number.Stream Methods infinite :: Closure Stream Rational Source #
Infinitary (Closure Stream R) Source #
Instance details Defined in Math.Number.R Methods infinite :: Closure Stream R Source #
Infinitary (Closure Stream R) Source #
Instance details Defined in Math.Number.Real Methods infinite :: Closure Stream R Source #
Infinitary (Closure Stream Integer) Source #
Instance details Defined in Math.Number.Stream Methods infinite :: Closure Stream Integer Source #
(Show (Closure Stream r), Eq (Closure Stream r)) => Eq (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (==) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (/=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool #
(Show (Closure Stream r), Num (Closure Stream r), Ord (Closure Stream r)) => Ord (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods compare :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Ordering # (<) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (<=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (>) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (>=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # max :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # min :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) #
(Closed a, RealFloat a) => Floating ((Stream :*: Complex) a) Source #
Instance details Defined in Math.Number.Complex Methods pi :: (Stream :: Complex) a # exp :: (Stream :: Complex) a -> (Stream :: Complex) a # log :: (Stream :: Complex) a -> (Stream :: Complex) a # sqrt :: (Stream :: Complex) a -> (Stream :: Complex) a # () :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # logBase :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # sin :: (Stream :: Complex) a -> (Stream :: Complex) a # cos :: (Stream :: Complex) a -> (Stream :: Complex) a # tan :: (Stream :: Complex) a -> (Stream :: Complex) a # asin :: (Stream :: Complex) a -> (Stream :: Complex) a # acos :: (Stream :: Complex) a -> (Stream :: Complex) a # atan :: (Stream :: Complex) a -> (Stream :: Complex) a # sinh :: (Stream :: Complex) a -> (Stream :: Complex) a # cosh :: (Stream :: Complex) a -> (Stream :: Complex) a # tanh :: (Stream :: Complex) a -> (Stream :: Complex) a # asinh :: (Stream :: Complex) a -> (Stream :: Complex) a # acosh :: (Stream :: Complex) a -> (Stream :: Complex) a # atanh :: (Stream :: Complex) a -> (Stream :: Complex) a # log1p :: (Stream :: Complex) a -> (Stream :: Complex) a # expm1 :: (Stream :: Complex) a -> (Stream :: Complex) a # log1pexp :: (Stream :: Complex) a -> (Stream :: Complex) a # log1mexp :: (Stream :: Complex) a -> (Stream :*: Complex) a #
RealFloat a => Num ((Stream :*: Complex) a) Source #
Instance details Defined in Math.Number.Complex Methods (+) :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # (-) :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # () :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # negate :: (Stream :: Complex) a -> (Stream :: Complex) a # abs :: (Stream :: Complex) a -> (Stream :: Complex) a # signum :: (Stream :: Complex) a -> (Stream :: Complex) a # fromInteger :: Integer -> (Stream :*: Complex) a #
RealFloat a => Fractional ((Stream :*: Complex) a) Source #
Instance details Defined in Math.Number.Complex Methods (/) :: (Stream :: Complex) a -> (Stream :: Complex) a -> (Stream :: Complex) a # recip :: (Stream :: Complex) a -> (Stream :: Complex) a # fromRational :: Rational -> (Stream :: Complex) a #
PpShow a => Show ((Stream :*: Stream) a) Source #
Instance details Defined in Math.Number.Stream Methods showsPrec :: Int -> (Stream :: Stream) a -> ShowS # show :: (Stream :: Stream) a -> String # showList :: [(Stream :*: Stream) a] -> ShowS #
ConjugateSymmetric a => ConjugateSymmetric ((Stream :*: Stream) a) Source #
Instance details Defined in Math.Number.Stream Methods conj :: (Stream :: Stream) a -> (Stream :: Stream) a Source #
data Codiagonal Stream a Source #
Instance details Defined in Math.Number.StreamInterface data Codiagonal Stream a = CodiagonalStream { codiagonal_substreams :: Stream (Stream a, Stream a) }
type Vector2 :+: Stream Source #
Instance details Defined in Math.Matrix.VectorConversions type Vector2 :+: Stream = Stream
type Vector3 :+: Stream Source #
Instance details Defined in Math.Number.Stream type Vector3 :+: Stream = Stream
type Stream \\ a Source #
Instance details Defined in Math.Number.StreamInterface type Stream \\ a = Stream a
data Closure Stream Rational Source #
Instance details Defined in Math.Number.Stream data Closure Stream Rational = FiniteRational (Stream Rational) \| MinusInfiniteRational \| InfiniteRational
data Closure Stream R Source #
Instance details Defined in Math.Number.R data Closure Stream R = RClosure { runRClosure :: !R }
data Closure Stream R Source #
Instance details Defined in Math.Number.Real data Closure Stream R = RClosure { runRClosure :: R }
data Closure Stream Integer Source #
Instance details Defined in Math.Number.Stream data Closure Stream Integer = FiniteInteger { integer_closure_stream :: Stream Integer } \| MinusInfiniteInteger \| InfiniteInteger
data Closure Stream Double Source #
Instance details Defined in Math.Number.Stream data Closure Stream Double = DoubleClosure (Stream Double) \| InfiniteDouble \| MinusInfiniteDouble \| NegativeZeroDouble \| NaNDouble \| DenormalizedDouble
data Closure Stream Float Source #
Instance details Defined in Math.Number.Stream data Closure Stream Float = FloatClosure (Stream Float) \| InfiniteFloat \| MinusInfiniteFloat \| NegativeZeroFloat \| NaNFloat \| DenormalizedFloat
data Closure Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis data Closure Stream (Quantity r) = QuantityClosure (Closure Stream r) Dimension
data Closure Stream (Stream a) Source #
Instance details Defined in Math.Number.Stream data Closure Stream (Stream a) = SClosure { runSClosure :: Stream (Closure Stream a) stream_limit :: Closure Stream a }
data Closure Stream (IO ()) Source #
Instance details Defined in Math.Number.Stream data Closure Stream (IO ()) = IOClosure { runIOClosure :: IO () }
data Closure Stream (a :==: a) Source #
Instance details Defined in Math.Number.Stream data Closure Stream (a :==: a) = IsoClosure { runIsoClosure :: Stream (a :==: a) }
data Closure Stream (Kleisli m a a) Source #
Instance details Defined in Math.Number.Stream data Closure Stream (Kleisli m a a) = KleisliClosure { runKleisliClosure :: Kleisli m a a }
type Rep (Stream a) Source #
Instance details Defined in Math.Number.Stream type Rep (Stream a) = D1 ('MetaData "Stream" "Math.Number.StreamInterface" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "Pre" 'PrefixI 'True) (S1 ('MetaSel ('Just "shead_impl") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "stail_lazy") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Stream a))))
type Scalar (Stream a) Source #
Instance details Defined in Math.Number.StreamInterface type Scalar (Stream a) = a
data Fold (Stream a) b Source #
Instance details Defined in Math.Number.Stream data Fold (Stream a) b = StreamFold (a -> c -> b) (Fold (Stream a) c)
data Unfold (Stream a) b Source #
Instance details Defined in Math.Number.Stream data Unfold (Stream a) b = StreamUnfold (Unfold a b) (Unfold (Stream a) b)
type Scalar (Closure Stream R) Source #
Instance details Defined in Math.Number.Real type Scalar (Closure Stream R) = R

class Infinitesimal Stream a => Closed a where Source #

Methods

accumulation_point :: Closure Stream a -> a Source #

Instances

Instances details

Closed R Source #
Instance details Defined in Math.Number.R Methods accumulation_point :: Closure Stream R -> R Source #
Closed R Source #
Instance details Defined in Math.Number.Real Methods accumulation_point :: Closure Stream R -> R Source #
Closed Double Source #
Instance details Defined in Math.Number.Stream Methods accumulation_point :: Closure Stream Double -> Double Source #
Closed Float Source #
Instance details Defined in Math.Number.Stream Methods accumulation_point :: Closure Stream Float -> Float Source #
(RealFloat a, Infinitesimal Stream a) => Closed (Complex a) Source #
Instance details Defined in Math.Number.Stream Methods accumulation_point :: Closure Stream (Complex a) -> Complex a Source #
(Closed a, Show a) => Closed (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods accumulation_point :: Closure Stream (Quantity a) -> Quantity a Source #
(Closed a, Num a) => Closed (Stream a) Source #
Instance details Defined in Math.Number.Stream Methods accumulation_point :: Closure Stream (Stream a) -> Stream a Source #

type DerivateConstraint str a = (Monad str, Num a) Source #

partial_derivate :: (Closed eps, Fractional eps) => (eps -> a -> a) -> (a -> eps) -> a -> eps Source #

\[ {\rm{partial\_derivate}}(\Delta, f, x) = \lim_{\epsilon \rightarrow 0}{{f(\Delta_{\epsilon}(x)) - f(x)}\over{\Delta_{\epsilon}(x) - x}} \]

partial_derive :: (Closed a, Infinitesimal Stream a, Fractional a) => (a -> a -> a) -> (a -> a) -> a -> a Source #

\[ {\rm{partial\_derive}}(\Delta, f, x) = \lim_{\epsilon \rightarrow 0}{{f(\Delta_{\epsilon}(x)) - f(x)}\over{\Delta_{\epsilon}(x) - x}} \]

derivate_around :: Infinitesimal str a => (a -> a) -> a -> Closure str a Source #

derivate_around doesn't require f to be defined at x, but requires limits from both sides of x to exist [it never evaluates f at x]. \[ \lim_{\epsilon \rightarrow 0} {{f(x+\epsilon)-f(x-\epsilon)}\over{2\epsilon}} \]

vector_derivate :: (Infinitesimal str (Scalar a), VectorSpace a, Limiting str a) => (Scalar a -> a) -> Scalar a -> Closure str a Source #

derivate_closed :: Infinitesimal str a => (a -> a) -> a -> Closure str a Source #

newtons_method_real :: (Infinitesimal Stream a, Closed a) => (a -> a) -> a -> Closure Stream a Source #

iterate_stream :: StreamBuilder str => (a -> a) -> a -> str a Source #

pseudo_derivate :: (Fractional r, Limiting str r, Infinitesimal str a) => (a -> r) -> a -> Closure str r Source #

https://en.wikipedia.org/wiki/Differential_calculus

partial_derivate1_2 :: Infinitesimal str a => (a -> b -> a) -> a -> b -> Closure str a Source #

\[\lim_{\epsilon\rightarrow 0}{{f(a+\epsilon,b)-f(a,b)}\over{\epsilon}}\]

partial_derivate2_2 :: Infinitesimal str a => (b -> a -> a) -> b -> a -> Closure str a Source #

\[\lim_{\epsilon\rightarrow 0}{{f(a,b+\epsilon)-f(a,b)}\over{\epsilon}}\]

partial_derivate1_3 :: Infinitesimal str a => (a -> b -> c -> a) -> a -> b -> c -> Closure str a Source #

\[\lim_{\epsilon\rightarrow 0}{{f(a+\epsilon,b,c)-f(a,b,c)}\over{\epsilon}}\]

partial_derivate2_3 :: Infinitesimal str a => (b -> a -> c -> a) -> b -> a -> c -> Closure str a Source #

\[\lim_{\epsilon\rightarrow 0}{{f(a,b+\epsilon,c)-f(a,b,c)}\over{\epsilon}}\]

partial_derivate3_3 :: Infinitesimal str a => (b -> c -> a -> a) -> b -> c -> a -> Closure str a Source #

\[\lim_{\epsilon\rightarrow 0}{{f(a,b,c+\epsilon)-f(a,b,c)}\over{\epsilon}}\]

constant :: a -> Stream a Source #

stream consisting of the same element repeated.

stream_matrix_impl :: Stream a -> Stream (Stream a, Stream a) -> (Stream :*: Stream) a Source #

stream_diagonal_impl :: (Stream :*: Stream) a -> Stream a Source #

stream_codiagonal_impl :: (Stream :*: Stream) a -> Stream (Stream a, Stream a) Source #