AutoDiff Example for PHY 604

This is a simple example of forward autodiff for PHY 604 (Graduate Computing II). We live-coded most of the scaffolding in class today; but after class I cleaned up the type promotion and added a bunch of examples and tests. The ForwardAutodiff.ipynb notebook has some comments and tries to explain what the code is doing.

For proper use we will want a library that we can import and use, so I extracted the code and put it into a module (and the tests in an automated test suite, too). If you would like to try it in your code, fire up Julia, enter the package mode (press ]), and enter the command

add https://github.com/Farr-PHY-604/ForwardAutodiff.jl.git

that will download this package and add it to the package manifest for the currently-active environment. Then you can do cool stuff like

using ForwardAutodiff

cos_from_derivative = D(sin)

print(cos_from_derivative(1.234) - cos(1.234))  # Should be close to zero

cycloid_tangent_vector = D(t -> [cos(2*pi*t), sin(2*pi*t) t])
print(cycloid_tangent_vector(2)) # It points somewhere...

Forward-mode autodiff is efficient for functions from R to R or R to R^N; if you have a function from R^N to R, check out the partner BackwardAutodiff module, which can efficiently compute gradients of R^N to R functions.

TODO: permit differentiation wrt more than one variable at a time (i.e. D(D(sin)) = sin). Expand derivatives to more functions. Maybe implement backward Autodiff? More stress testing!

Note: if you just want to run the tests for this package, then clone the git repo, enter the top-level directory, fire up Julia, enter package mode (type ]), and then

test

Julia knows to run the test/runtests.jl program in the correct environment. Everything should pass, of course!