Support complex types

[unnonouno]

Currently Chainer assumes integers and floating point numbers. Now CuPy supports complex numbers. It's time to support complex numbers in Chainer.

• Support complex numbers in gradient check
• Support complex numbers in various functions

[m3at]

I'm curious about this, do you already have use-cases in mind or is that to broaden the capabilities of Chainer?
I see your related ongoing PR, does that target the reproduction of a specific paper?

[unnonouno]

Yes. Some research papers use complex numbers or FFT. And i think it can be applied for speech processing. I want to improve capability of Chainer.

• https://arxiv.org/abs/1511.06464
• https://arxiv.org/abs/1611.00035
• http://www.aclweb.org/anthology/D16-1044

[m3at]

Understood.
Thanks for the papers, I didn't know about the last two, seems very interesting!
Looking forward to use it in Chainer 👍

[hknerdgn]

You should definitely look into https://arxiv.org/pdf/1701.00392.pdf as well.

[unnonouno]

Thank you for a link!! Please thumb up this issue if you guys need this feature.

[toslunar]

Should Chainer support "complex32" whose real/imag part is float16? It seems NumPy hasn't yet support "complex32".

[unnonouno]

IMO, no, especially for the first implementation.

[shivam7569]

I would like to work on this. Could anyone guide me with the process? Thanks!