Support for complex numbers

[AlexanderKoshkarov]

It would be nice if the package would support the complex numbers. Probably it is difficult to check when the derivative exist, and what path to take on the complex plane to take derivative. However if you will make default derivative path (for example along real axis) it should be good enough (I think) for DifferentialEquations.jl by @ChrisRackauckas where derivatives are used to calculate Jacobian in implicit ODE integrators.
If it would be possible to indicate the curve on complex plane where to take derivative, it also would be awesome. Thanks.

[ChrisRackauckas]

It seems that Complex64 doesn't have eps defined which interferes with step_size. If that was somehow avoided, would the routines theoretically work correctly? Or is there a difficulty I'm not seeing?

I think always taking the derivative along the real axis is fine because if the function is complex differentiable then it's path independent.

[johnmyleswhite]

Sorry, I was unclear in the other repository. I do not accept feature requests. If you are interested in writing code that provides this functionality, I will review a pull request.

You should find all the information you need to implement such a pull request here: http://deeplearning.net/software/theano/proposals/complex_gradient.html

[AlexanderKoshkarov]

Sorry for the confusion. Thanks for the link.

[ChrisRackauckas]

The final solution on this was to create DiffEqDiffTools.jl which handles this case.