This is a library for automatic differentiation in Clojure. It's based
and initiall ported from R6RS-AD
and clj-auto-diff.
At the moment library is not in Clojars (yet). So, you will need to
fork the repository and do lein install in the repo directory. After
this the project can be referenced using
[clj-ad "0.2.0"]
in dependencies. More info on using Leiningen with local repository can be found here.
AD rerers to the method of calculating numerical derivatives analytically, but not symbolically. A general idea is to exploit the chain rule. For this the whole arithmetic of the language is replaced with slightly more generic arithmetic operations: instead of operating on numbers only, these operations can accept dual numbers or tapes and produce the derivative of the operation as well as the main result.
In essence, dual numbers are the extension of numbers with
perturbations, their "derivatives". Consider function f(x). If we
know it's derivative df(x), then given a dual number [z dz], the
result of application of f(x) to it is a dual number
[f(z) df(z)*dz]. This result can become an input to the next
function g(x), producing [g(f(z)) dg(z)*df(z)*dz]. And so on. To
begin the process, all we need is to set dz=1. This is called
forward derivative.
TODO: reverse derivative.
Forward derivatives are implemented in full. Reverse derivatives still need to be implemented.
Next step: implement full Jacobian calculation.
TODO
TODO
TODO
Copyright © 2014 Paul English Copyright © 2016 Alexey Cherkaev (mobius-eng)
Distributed under the Eclipse Public License either version 1.0 or (at your option) any later version.