Implement norm on vectors with custom metric

[FrederikLauber]

Hello,

it would be great if we could get a norm on the vector with a custom metric.
As a physicist, having the possibility to use a minkowski metric or similar would be very nice.

Thanks in advance

[sebcrozet]

Hi!

That would be a great addition. Which metric do you think nalgebra should provide by default? (Besides the metrics induced by the p-norms.)

[FrederikLauber]

I would argue none because most problems will have their very own metric.
Minkowski is used quite a lot in special relativity but if there is no significant speed boost,
I would the user just define its own.

I also already tried to get this working but am apparently not good enough in rust to constrain
the input vector and input metric to the same dimensions.

[sebcrozet]

I agree we should let the user define its own specific metric. If you want to try implementing this, you may draw some inspiration from the dot product method. It has the dimensional constraints that you need.