Automatic (algorithmic) differentiation library for Common Lisp. It is based on Scheme library but is implemented in a more generic way using CLOS.
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 - complete, beta-state Reverse derivatives - TODO
- Extend it to symbolic data
- Implement full Jacobian calculation
Copyright © 2016 Alexey Cherkaev (mobius-eng)
Distributed under Lesser GNU Public License 3 or (at your option) any later version.