Portability GHC only experimental ekmett@gmail.com None

Description

Forward mode automatic differentiation

Synopsis

grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f aSource

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

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

# 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

Compute the Jacobian using `Forward` mode `AD`. This must transpose the result, so `jacobianT` is faster and allows more result types.

````>>> ````jacobian (\[x,y] -> [y,x,x+y,x*y,exp x * sin y]) [pi,1]
```[[0.0,1.0],[1.0,0.0],[1.0,1.0],[1.0,3.141592653589793],[19.472221418841606,12.502969588876512]]
```

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

Compute the Jacobian using `Forward` mode `AD` along with the actual answer.

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

Compute the Jacobian using `Forward` mode `AD` combined with the input using a user specified function, along with the actual answer.

# 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

A fast, simple, transposed Jacobian computed with `Forward` mode `AD` that combines the output with the input.

# 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

# Derivatives

diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> aSource

The `diff` function calculates the first derivative of a scalar-to-scalar function by forward-mode `AD`

````>>> ````diff sin 0
```1.0
```

diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)Source

The `diff'` function calculates the result and first derivative of scalar-to-scalar function by `Forward` mode `AD`

``` `diff'` `sin` == `sin` `&&&` `cos`
`diff'` f = f `&&&` d f
```
````>>> ````diff' sin 0
```(0.0,1.0)
```
````>>> ````diff' exp 0
```(1.0,1.0)
```

diffF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f aSource

The `diffF` function calculates the first derivatives of scalar-to-nonscalar function by `Forward` mode `AD`

````>>> ````diffF (\a -> [sin a, cos a]) 0
```[1.0,-0.0]
```

diffF' :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)Source

The `diffF'` function calculates the result and first derivatives of a scalar-to-non-scalar function by `Forward` mode `AD`

````>>> ````diffF' (\a -> [sin a, cos a]) 0
```[(0.0,1.0),(1.0,-0.0)]
```

# 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

duF :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g aSource

Compute a vector of directional derivatives for a function given a zipped up `Functor` of the input values and their derivatives.

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)Source

Compute a vector of answers and directional derivatives for a function given a zipped up `Functor` of the input values and their derivatives.