mdspan VS stdBLAS

Why not use https://github.com/kokkos/mdspan though ?

It can be the base of whatever *you* write via bindings generators like pybind11. In that sense, the answer to your question is "however you like". For actual simulation code, you'll see a lot more legacy Fortran and C. That said, with things like mdspan maybe being standardized (proposal), efforts towards a standard linear algebra library, and the existence of ubiquitous HPC frameworks already having been written in C++, I would say it's only a matter of time before C++ accounts for an even bigger share of all HPC code.

I'm aware of only two relevant projects myself, I don't know much, came to reddit kind of by chance. One of the multi-dimensional array libraries proposed for potential standardisation, and a gnu machine learning library that was discontinued which could be worked off of. There's probably a lot more out there, but don't get distracted from making something awesome :)

As u/IyeOnline already made the important points about VLAs and std::vector, I would just add that you may find std::mdspan to be a helpful data structure. You can allocate 1d memory and give it a 2d shape of k with nice 2d indexing, eg auto& elem = mymdspan(row, col);.

Kokkos mdspan

The good thing here is that it heavily relies on mdpsan that is a multidimensional view that handle shape and strides. And kokkos provide a C++14 compatible implementation with a complete CUDA support.

You can have a look at https://github.com/kokkos/stdBLAS (it's an implementation of the proposed linear algebra extensions for future C++).

It has the same BSD license as Kokkos: https://github.com/kokkos/stdBLAS/blob/main/LICENSE

The BLAS and LAPACK have C interfaces, and they generally don't allocate memory unless you ask them. (Some BLAS implementations allocate internal storage for rearranging matrix data.) There are a few C++ BLAS wrappers; here is one of them.

The second one is stdBLAS by kokkos. It doesn't even use cuBLAS but it's a reference implementation of P1673. This paper describe what could be a blas API in the std. I would recommend trying to do something equivalent on your side.