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https://github.com/rajasharan/elm-automatic-differentiation
Automatic differentiation (a.k.a algorithmic differentiation) in reverse mode for elm
https://github.com/rajasharan/elm-automatic-differentiation
algorithmic-differentiation automatic-differentiation backpropagation elm elm-lang
Last synced: about 1 month ago
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Automatic differentiation (a.k.a algorithmic differentiation) in reverse mode for elm
- Host: GitHub
- URL: https://github.com/rajasharan/elm-automatic-differentiation
- Owner: rajasharan
- License: mit
- Created: 2017-11-05T16:48:12.000Z (about 7 years ago)
- Default Branch: master
- Last Pushed: 2017-11-05T16:50:47.000Z (about 7 years ago)
- Last Synced: 2024-09-30T05:23:01.703Z (about 2 months ago)
- Topics: algorithmic-differentiation, automatic-differentiation, backpropagation, elm, elm-lang
- Language: Elm
- Homepage:
- Size: 5.86 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
## Automatic differentiation in reverse mode for elm
This library calculates the paritial derivatives of a multi-variable function
using the method of automatic differentiation in reverse mode. The result is returned
as a dictionary of keys and their corresponding derivative values (gradient vector).
- a.k.a [algorithmic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation)
- a.k.a [backpropagation](https://en.wikipedia.org/wiki/Backpropagation)
## Usage
### Install
```sh
elm-package install rajasharan/elm-automatic-differentiation
```
### Import
```elm
import Dict exposing (Dict)
import AD.Reverse as AD
exposing
( pow, sqr, exp
, add, mul
, (|+|), (|.|), (|*|), (|^|)
, autodiff
)
```
### API usage
```elm
-- build a computation graph for your function, for e.g.,
-- f(x,y) = (x+y)^2 . e^(2.(y+1)) + sin (x+y)^2
f : Float -> Float -> AD.Node
f x y =
let
a = AD.Variable "x" x
b = AD.Variable "y" y
u = pow (a |+| b) (AD.Const 2)
v = (b |+| AD.Const 1)
w = sqr (exp v)
z = u |*| w |+| AD.sin u
in
z
-- result is a dictionary of keys and their corresponding derivative values
result : Dict String Float
result = autodiff (f 3 2)
-- [("x",4044.1999630459845),("y",24215.639637682732)]
-- this means:
-- ∂f/∂x = 4044.19996 at (x=3, y=2)
-- ∂f/∂y = 24215.6396 at (x=3, y=2)
```
#### Another example
```elm
-- g(x) = x^2
g : Float -> AD.Node
g x =
let
a = AD.Variable "x" x
in
a |^| (AD.Const 2)
result2 = autodiff (g 6)
-- [("x", 12)]
-- ∂g/∂x = 12 at (x=6)
```
## Further Reading
* [Rufflewind's Scratchpad - Reverse-mode automatic differentiation: a tutorial](https://rufflewind.com/2016-12-30/reverse-mode-automatic-differentiation)
* [Daniel Brice - Automatic Differentiation in Haskell](https://www.youtube.com/watch?v=q1DUKEOUoxA)
* [github.com/friedbrice/AutoDiff](https://github.com/friedbrice/AutoDiff)
### [License](/LICENSE)
The MIT License (MIT)