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| Data.Derivative | | Stability | experimental | | Maintainer | conal@conal.net |
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| Description |
| This module is a wrapper around Data.Maclaurin or Data.Horner, to
change the VectorSpace instance for '(:>)'.
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| Synopsis |
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| data a :> b | | | powVal :: (a :> b) -> b | | | derivative :: (VectorSpace b s, LMapDom a s) => (a :> b) -> a :-* (a :> b) | | | derivativeAt :: (LMapDom a s, VectorSpace b s) => (a :> b) -> a -> a :> b | | | type :~> a b = a -> a :> b | | | dZero :: (LMapDom a s, VectorSpace b s) => a :> b | | | pureD :: (LMapDom a s, VectorSpace b s) => b -> a :> b | | | (<$>>) :: (LMapDom a s, VectorSpace b s) => (b -> c) -> (a :> b) -> a :> c | | | liftD2 :: (VectorSpace b s, LMapDom a s, VectorSpace c s, VectorSpace d s) => (b -> c -> d) -> (a :> b) -> (a :> c) -> a :> d | | | liftD3 :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace d s, VectorSpace e s) => (b -> c -> d -> e) -> (a :> b) -> (a :> c) -> (a :> d) -> a :> e | | | idD :: (LMapDom u s, VectorSpace u s) => u :~> u | | | fstD :: (VectorSpace a s, LMapDom b s, LMapDom a s) => (a, b) :~> a | | | sndD :: (VectorSpace b s, LMapDom b s, LMapDom a s) => (a, b) :~> b | | | linearD :: (LMapDom u s, VectorSpace v s) => (u -> v) -> u :~> v | | | distrib :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace u s) => (b -> c -> u) -> (a :> b) -> (a :> c) -> a :> u | | | (@.) :: (LMapDom b s, LMapDom a s, VectorSpace c s) => (b :~> c) -> (a :~> b) -> a :~> c | | | (>-<) :: (LMapDom a s, VectorSpace s s, VectorSpace u s) => (u -> u) -> ((a :> u) -> a :> s) -> (a :> u) -> a :> u |
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| Documentation |
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| Tower of derivatives.
|  Instances | | Eq b => Eq (a :> b) | | (VectorSpace b b, LMapDom a b, Floating b) => Floating (a :> b) | | (VectorSpace b b, LMapDom a b, Fractional b) => Fractional (a :> b) | | (VectorSpace b b, LMapDom a b, Num b) => Num (a :> b) | | Ord b => Ord (a :> b) | | Show b => Show (a :> b) | | (VectorSpace b s, LMapDom a s) => AdditiveGroup (a :> b) | | (LMapDom a s, VectorSpace v s, HasCross3 v) => HasCross3 (a :> v) | | (LMapDom a s, VectorSpace v s, HasCross2 v) => HasCross2 (a :> v) | | (Num s, LMapDom s s) => HasNormal (Two s :> Three s) | | (Num s, LMapDom s s) => HasNormal (One s :> Two s) | | (InnerSpace u s, InnerSpace s s', VectorSpace s s, LMapDom a s) => InnerSpace (a :> u) (a :> s) | | (LMapDom a s, VectorSpace u s, VectorSpace s s) => VectorSpace (a :> u) (a :> s) |
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| Extract the value from a derivative tower
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| Extract the derivative from a derivative tower
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| Sampled derivative. For avoiding an awkward typing problem related
to the two required VectorSpace instances.
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| Infinitely differentiable functions
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| Derivative tower full of zeroV.
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| Constant derivative tower.
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| Map a linear function over a derivative tower.
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| Apply a linear binary function over derivative towers.
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| Apply a linear ternary function over derivative towers.
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| Differentiable identity function. Sometimes called the
derivation variable or similar, but it's not really a variable.
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| Differentiable version of fst
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| Differentiable version of snd
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| Every linear function has a constant derivative equal to the function
itself (as a linear map).
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| Derivative tower for applying a binary function that distributes over
addition, such as multiplication. A bit weaker assumption than
bilinearity.
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| Chain rule.
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| Specialized chain rule.
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| Produced by Haddock version 2.3.0 |
