|
Data.Maclaurin | Stability | experimental | Maintainer | conal@conal.net |
|
|
|
Description |
Infinite derivative towers via linear maps, using the Maclaurin
representation. See blog posts http://conal.net/blog/tag/derivatives/.
|
|
Synopsis |
|
data a :> b | | powVal :: :> a b -> b | | derivative :: :> a b -> a :-* (a :> b) | | derivativeAt :: (VectorSpace b s, LMapDom a s) => (a :> b) -> a -> a :> b | | type :~> a b = a -> a :> b | | dZero :: (LMapDom a s, AdditiveGroup b) => a :> b | | pureD :: (LMapDom a s, AdditiveGroup b) => 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 | | (**^) :: (VectorSpace c s, VectorSpace s s, LMapDom a s) => (a :> s) -> (a :> c) -> a :> c | | (<*.>) :: (LMapDom a s, InnerSpace b s, VectorSpace s s) => (a :> b) -> (a :> b) -> a :> s |
|
|
Documentation |
|
|
Tower of derivatives.
| Instances | |
|
|
|
|
|
|
|
Sampled derivative. For avoiding an awkward typing problem related
to the two required VectorSpace instances.
|
|
|
Infinitely differentiable functions
|
|
|
Derivative tower full of zeroV.
|
|
|
Constant derivative tower.
|
|
|
Map a linear function over a derivative tower.
|
|
|
Apply a linear binary function over derivative towers.
|
|
|
Apply a linear ternary function over derivative towers.
|
|
|
Differentiable identity function. Sometimes called the
derivation variable or similar, but it's not really a variable.
|
|
|
Differentiable version of fst
|
|
|
Differentiable version of snd
|
|
|
Every linear function has a constant derivative equal to the function
itself (as a linear map).
|
|
|
Derivative tower for applying a binary function that distributes over
addition, such as multiplication. A bit weaker assumption than
bilinearity.
|
|
|
Chain rule. See also '(>-<)'.
|
|
|
Specialized chain rule. See also '(@.)'
|
|
|
|
|
|
Produced by Haddock version 2.3.0 |