I think you might want to look at the Tensor library that I made a while back, which allows for vectors, matrices and any higher-order tensors as well. It works with sparse maps, making it more efficient when it is only partially filled. It probably provides the functionality you want (a multitude of different ways of filtering, adding/removing rows or colums, flipping or rotating, fast access to a single element, row or column, easy ways to sort rows or columns, etc).

It is of course also available on Hex.pm.

Extracting a single row or column I think is most efficient by using Enum.filter/2. This would make extracting a single column or row O(row * colums) though.

If you really need O(1) access to a complete row or column randomly, I do think, that a doubled DS would be the only thing to go, but it does double the amount of memory needed to hold the structure, also it makes writes expensive since they had to be done twice.

Basically you need to two nested maps %{row_id => %{col_id => data_sample}} and %{col_id => %{row_id => data_sample}}.

Yeah the duplication is definitely a possibility. Fortunately this is less duplication than it may look at first glance because cell values are just pointed to by each map location, not actually duplicated.

:ets could be another possibility because it does support a {_, 1} style match operation.

FWIW even traditional mutable 2d arrays suffer from this question. If you make row access primary then column access requires large jumps in memory which eats away at any cache locality you may have gotten with row access.