Copyright (c) Edward Kmett 2010-2015 BSD3 ekmett@gmail.com experimental GHC only None Haskell2010

Description

Forward Mode AD specialized to `Double`. This enables the entire structure to be unboxed.

Synopsis

# Documentation

Instances

grad :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f Double Source

Note, this performs O(n) worse than `grad` for `n` inputs, in exchange for better space utilization.

grad' :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, f Double) Source

Note, this performs O(n) worse than `grad'` for `n` inputs, in exchange for better space utilization.

gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f b Source

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 => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, 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.

````>>> ````gradWith' (,) sum [0..4]
```(10.0,[(0.0,1.0),(1.0,1.0),(2.0,1.0),(3.0,1.0),(4.0,1.0)])
```

# Jacobian

jacobian :: (Traversable f, Traversable g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (f Double) 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) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, f Double) Source

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

jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> 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) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, 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) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g Double) Source

A fast, simple, transposed Jacobian computed with forward-mode AD.

jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g b) Source

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

# Derivatives

diff :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> Double Source

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

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

diff' :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> (Double, Double) 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 => (forall s. AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f Double Source

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 => (forall s. AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f (Double, Double) 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 => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> Double Source

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

du' :: Functor f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> (Double, Double) 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) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g Double Source

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) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g (Double, Double) Source

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