Portability | GHC only |
---|---|
Stability | experimental |
Maintainer | ekmett@gmail.com |
Safe Haskell | Safe-Infered |
Forward mode automatic differentiation
- grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
- grad' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)
- gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f b
- gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)
- jacobian :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
- jacobian' :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f a)
- jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)
- jacobianWith' :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)
- jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g a)
- jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g b)
- hessianProduct :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f a
- hessianProduct' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f (a, a)
- diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diffF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
- diffF' :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)
- du :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> a
- du' :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)
- duF :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g a
- duF' :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g (a, a)
Gradient
grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f aSource
Compute the gradient of a function using forward mode AD.
Note, this performs O(n) worse than grad
for n
inputs, in exchange for better space utilization.
grad' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)Source
Compute the gradient and answer to a function using forward mode AD.
Note, this performs O(n) worse than grad'
for n
inputs, in exchange for better space utilization.
gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f bSource
Compute the gradient of a function using forward mode AD and combine the result with the input using a user-specified function.
Note, this performs O(n) worse than gradWith
for n
inputs, in exchange for better space utilization.
gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)Source
Compute the gradient of a function using forward mode AD and the answer, and combine the result with the input using a user-specified function.
Note, this performs O(n) worse than gradWith'
for n
inputs, in exchange for better space utilization.
Jacobian
jacobian :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)Source
jacobian' :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f a)Source
jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)Source
Compute the Jacobian using Forward
mode AD
and combine the output with the input. This must transpose the result, so jacobianWithT
is faster, and allows more result types.
jacobianWith' :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)Source
Transposed Jacobian
jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g a)Source
A fast, simple, transposed Jacobian computed with forward-mode AD.
jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g b)Source
Hessian Product
hessianProduct :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f aSource
Compute the product of a vector with the Hessian using forward-on-forward-mode AD.
hessianProduct' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f (a, a)Source
Compute the gradient and hessian product using forward-on-forward-mode AD.
Derivatives
Directional Derivatives
du :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> aSource
Compute the directional derivative of a function given a zipped up Functor
of the input values and their derivatives
du' :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)Source
Compute the answer and directional derivative of a function given a zipped up Functor
of the input values and their derivatives