This is an alternative site for discovering Elm packages.
You may be looking for the
official Elm package site
instead.

Automatic differentiation (a.k.a algorithmic differentiation) in reverse mode

version | 1.0.0 |

license | MIT |

native-modules | False |

elm-version | 0.18.0 <= v < 0.19.0 |

Tag | 1.0.0 |

Committed At | 2017-11-05 16:46:47 UTC |

elm-lang/core | 5.1.1 <= v < 6.0.0 | 5.1.1 |

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
- a.k.a backpropagation

```
elm-package install rajasharan/elm-automatic-differentiation
```

```
import Dict exposing (Dict)
import AD.Reverse as AD
exposing
( pow, sqr, exp
, add, mul
, (|+|), (|.|), (|*|), (|^|)
, autodiff
)
```

```
-- 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)
```

```
-- 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)
```

- Rufflewind's Scratchpad - Reverse-mode automatic differentiation: a tutorial
- Daniel Brice - Automatic Differentiation in Haskell
- github.com/friedbrice/AutoDiff

The MIT License (MIT)