Support for Sparse Algebras about clifford

[moble]

I'd just like to suggest that since Cl is pretty much the main callable in this library, it might be helpful to have a more descriptive name for the new argument. Maybe desired_grades or even just grades?

[hugohadfield]

Thanks for the table @enkimute interesting how fast the javascript startup times are!
just added to my PR here: #43
this should bring the start up times down very significantly

[hugohadfield]

Thanks for the detailed issue @Stefan-Endres ! High dimensional algebra support is a big priority for us at the moment as it is the biggest performance killer in this library at the moment and people are interested in it, it would be great to get your contributions.
I have been thinking about our problems here for a little while, check out #17
I'm just digging into this even odd issue now and it is pretty nasty

[hugohadfield]

Ok, this commit adds a bit of speedup and hopefully simplifies the code a little as a start for us to understand what is going on!
f67bcef

[hugohadfield]

These even and odd permutation tables appear to be used only in _gmtElement. I think modifying _genEvenOdd to use your kr parameter and limiting the for i in range(self.gaDims): to the indices of your sparse algebra will work fine and will bring big speedups

[Stefan-Endres]

Wow! Thank you, it's already much faster. I'm going to play around with weaving kr into the _genEvenOdd loop hopefully we can squeeze even more speed out of a sparse initialization.

[hugohadfield]

Fantastic, drop us a PR when you are ready and we can merge it in

[enkimute]

Just for comparison, ganja.js absolutely not optimized generation times :

1-dimensional clifford: 0.674072265625ms
2-dimensional clifford: 0.808837890625ms
3-dimensional clifford: 2.743896484375ms
4-dimensional clifford: 10.283935546875ms
5-dimensional clifford: 22.559814453125ms
6-dimensional clifford: 83.708984375ms
7-dimensional clifford: 439.293212890625ms
8-dimensional clifford: 2795.296875ms
9-dimensional clifford: 18897.85400390625ms

[enkimute]

After fixing some very obvious things :

1-dimensional clifford: 0.63427734375ms
2-dimensional clifford: 0.7509765625ms
3-dimensional clifford: 1.22021484375ms
4-dimensional clifford: 3.337158203125ms
5-dimensional clifford: 11.001953125ms
6-dimensional clifford: 38.415283203125ms
7-dimensional clifford: 148.318115234375ms
8-dimensional clifford: 603.589599609375ms
9-dimensional clifford: 2689.2021484375ms
10-dimensional clifford: 11346.662841796875ms

[hugohadfield]

@Stefan-Endres with the latest release of the library we are in a place where higher dimensional algebra initialisation is pretty fast, do you think sparse algebra support is still necessary? Or should we close the issue?

[Stefan-Endres]

I think it would be better to close the issue for now. The last time I worked on this I was not able to make all the desirable operations work seamlessly, what I did relies on some very ugly/unmaintanable hacks. If I find a better solution some day I'll open a new PR if there are applications requiring very high dimensions (meaning to the point where the memory requirements of combinatorial growth of the blades of "middle" grades are intractable) and/or a good maintainable solution, but for now I don't think it would benefit the library (on a personal note it's working really well for my applications at the moment as I do not use extremely high dimensions).

Thanks for the great work on the initialisation improvements!

[hugohadfield]

:) glad it is working out for you, it's nice to see this library being used in some wider applications!