Automatic Differentiation for JavaScript

A translation of the ad library from Jeff Siskind's Qobischeme.

Some links that explain what AD is:

• Wikipedia
• Introduction to Automatic Differentiation

This package provides

• transformed functions and means to transform others
• sweetjs macros that can be used to effect replacement of primitive functions with above transformed/overloaded ones.

Usage

Install as npm install ad.js

Use sweet to load the macros and compile code

var sweet = require('sweet.js');
var adMacros = sweet.loadNodeModule(null, 'ad.js/macros')
var adLoadString = "var ad = require('ad.js')({});\n";
var _compiled = sweet.compile(<your-file-contents>, {modules: adMacros});
var compiled = adLoadString + _compiled.code

Also, the ad require statement must be passed options. To get the default behaviour:

var ad = require('ad.js')({})

To run only reverse mode (faster)

var ad = require('ad.js')({mode: 'r'})

To run only reverse mode with only first-derivatives (faster even)

var ad = require('ad.js')({mode: 'r', noHigher: true})

Test

Uses nodeunit. To run tests, do npm test

Example

The setup takes a file that looks like so:

var cube = function(x) {
  return x * x * x;
}

and transforms it into code that looks like so:

var cube = function(x) {
  return ad.mul(x, ad.mul(x, x));
}

after which one can do things like:

var dCube_dx = ad.derivativeF(cube);
console.log(dCube_dx(10))
// will print 300 => d/dx(x^3) = 3x^2 @x=10 = 300

and even higher-order derivatives as:

var d2Cube_dx2 = ad.derivativeF(dcube_dx);
console.log(d2Cube_dx2(10))
// will print 60 => d2/dx2(x^3) = 6x @x=10 = 60

The bulk of the instructions above are just the means by which sweet gets its hands on the code you want to transform and the macros to transform it with.