Safe Haskell | None |
---|---|

Language | Haskell2010 |

## Synopsis

- data ForwardDouble
- grad :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> f Double
- grad' :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f Double)
- gradWith :: Traversable f => (Double -> Double -> b) -> (f ForwardDouble -> ForwardDouble) -> f Double -> f b
- gradWith' :: Traversable f => (Double -> Double -> b) -> (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f b)
- jacobian :: (Traversable f, Traversable g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f Double)
- jacobian' :: (Traversable f, Traversable g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> g (Double, f Double)
- jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f b)
- jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (Double, f b)
- jacobianT :: (Traversable f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double)
- jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g b)
- diff :: (ForwardDouble -> ForwardDouble) -> Double -> Double
- diff' :: (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double)
- diffF :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f Double
- diffF' :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f (Double, Double)
- du :: Functor f => (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> Double
- du' :: Functor f => (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> (Double, Double)
- duF :: (Functor f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f (Double, Double) -> g Double
- duF' :: (Functor f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f (Double, Double) -> g (Double, Double)

# Documentation

data ForwardDouble Source #

## Instances

# Gradient

grad :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> f Double Source #

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 => (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f Double) 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 => (Double -> Double -> b) -> (f ForwardDouble -> 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) -> (f ForwardDouble -> 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.

`>>>`

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

# Jacobian

jacobian :: (Traversable f, Traversable g) => (f ForwardDouble -> g 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.

`>>>`

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

jacobian' :: (Traversable f, Traversable g) => (f ForwardDouble -> g 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) -> (f ForwardDouble -> g 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) -> (f ForwardDouble -> g 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) => (f ForwardDouble -> g 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) -> (f ForwardDouble -> g 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 :: (ForwardDouble -> ForwardDouble) -> Double -> Double Source #

The `diff`

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

`>>>`

1.0`diff sin 0`

diff' :: (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double) Source #

diffF :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f Double Source #

The `diffF`

function calculates the first derivatives of scalar-to-nonscalar function by `Forward`

mode `AD`

`>>>`

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

diffF' :: Functor f => (ForwardDouble -> f 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`

`>>>`

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

# Directional Derivatives

du :: Functor f => (f ForwardDouble -> 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 => (f ForwardDouble -> 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