In “normal” BEAM code, both arrays and floating-point values are expensive:

• a plain list like [0.1, 0.2, 0.3, 0.4] is a linked list, so it takes about 2x as long to access the 4th element as it does the second. This makes large lists like in simulations impossibly slow, adding an extra factor of N to runtimes in general. (good luck with multidimensional data )

• updating an element in the middle of a list is expensive, since it requires updating all the linked list cells before the element. This collides badly with a lot of scientific algorithms that assume that updating a value in-place is cheap.

• floating-point values themselves are expensive, because they are boxed

The boxing and the linked-list combined end up making a single element of a floating-point list like [1.0, 2.0, 3.0, 4.0] cost 28 bytes (on a 64-bit machine):

• two pointers for the cons cell
• a 4-byte header + 8-byte value for the float

Nx removes all that overhead, because it stores tensors with fixed datatype (u64, f32, etc) as contiguous blocks of memory. The Nx intro has more.

There’s a ton of other useful features for numerical computing in Nx, but even if all you used it for was to get constant-time access to multidimensonal arrays it’s a huge increase in Elixir’s capabilities.

I haven’t seen anything specific along those lines; Nx is new enough that it mostly has the features that somebody needed to get the thing done they wanted to do, so a lot of the focus has been on ML-adjacent problems and things that parallelize well to GPUs.

There’s some basic algorithms in Nx.LinAlg, but you won’t find optimizations like “store L and U from LU decomposition together in the same array to save space that would otherwise be zeroes” there.

On the positive side, that means there’s plenty of unclaimed library real-estate just waiting for an author to put some code in it!

One other option: since Nx stores values in contiguous blocks, it would be much easier to interface to a Serious Science numeric library with Rustler (versus trying to convert to and from linked-lists).

Scholar can also provide some examples/ideas: https://hexdocs.pm/scholar/Scholar.html