Million Magnet Simulation: Mathematica vs Python vs OpenGL

Follow me on twitter at GoldPlatedGoof

0:00:00 Start
0:01:27 Going over the math
0:03:53 Mathematica on the CPU
0:05:55 Broadcasting in NumPy
0:11:30 Shadertoy/OpenGL
0:15:19 Farewell

[Laff]

Mathematica has non-linear neural network functionality which can utilize the GPU. That, as well as FunctionCompile, could drastically speed it up.

[kenhaley]

Amazing stuff! I wish I'd seen the live stream.

I"ve been missing your streams ever since the start of 2022...not by choice though. I hope to make next Wednesday.

[jojojorisjhjosef]

This is epic though, especially the openGL one.

[ssquarkgaming]

Few very simple tricks to speed up this python code.
Replace divisions with multiplications. Especially that divide by 6 in that for loop.. Precompute 1/6 outside the loop and instead multiply by 1/6th.

Replace powers with multiplications.. Where possible ofcourse.. E.g. Instead of writing x**2, write x * x
Python is not a compiled language (well some IDEs can compile but not jupyter) so simple performance improvements like this will not be automatically done by a compiler.

Replace multiplications with addition or bit shifting. If you want to do 2 * x just write x + x it will be faster (especially in a loop as small gains stack up in loops) and in a situation where x is an integer you can use x << 1 to multiply by 2 and this is slightly faster than adding.

If I think of more improvements, hopefully better ones than this list.

And I will benchmark these changes and post a reply to this comment with the performance gain.. Which probably won't be much but these are nice to know improvements.

[ekamperi]

Why doesn't this have one million views?

[jojojorisjhjosef]

I will never understand why so many respected people who use python work in jupyter.

[fatfingersman]

Are you the math genius i have been looking for?